LMFDB - Embedded newform 273.2.t.d.205.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(4,273)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("273.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + \cdots + 576 $ x^20 + 33x^18 + 455x^16 + 3403x^14 + 15006x^12 + 39799x^10 + 62505x^8 + 55993x^6 + 27166x^4 + 6435*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.4
Root			$-0.871638i$ of defining polynomial
Character	$\chi$	$=$	273.205
Dual form			273.2.t.d.4.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.871638i q^{2} +(0.500000 - 0.866025i) q^{3} +1.24025 q^{4} +(1.34003 + 0.773665i) q^{5} +(-0.754861 - 0.435819i) q^{6} +(-2.02693 - 1.70046i) q^{7} -2.82432i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-0.871638i q^{2} +(0.500000 - 0.866025i) q^{3} +1.24025 q^{4} +(1.34003 + 0.773665i) q^{5} +(-0.754861 - 0.435819i) q^{6} +(-2.02693 - 1.70046i) q^{7} -2.82432i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.674356 - 1.16802i) q^{10} +(3.13150 + 1.80798i) q^{11} +(0.620123 - 1.07408i) q^{12} +(-3.37483 + 1.26906i) q^{13} +(-1.48218 + 1.76675i) q^{14} +(1.34003 - 0.773665i) q^{15} +0.0187042 q^{16} +4.63205 q^{17} +(-0.754861 + 0.435819i) q^{18} +(-0.508319 + 0.293478i) q^{19} +(1.66196 + 0.959535i) q^{20} +(-2.48610 + 0.905145i) q^{21} +(1.57590 - 2.72954i) q^{22} -2.28523 q^{23} +(-2.44594 - 1.41216i) q^{24} +(-1.30289 - 2.25666i) q^{25} +(1.10616 + 2.94163i) q^{26} -1.00000 q^{27} +(-2.51389 - 2.10899i) q^{28} +(1.07556 + 1.86293i) q^{29} +(-0.674356 - 1.16802i) q^{30} +(-8.99732 + 5.19461i) q^{31} -5.66495i q^{32} +(3.13150 - 1.80798i) q^{33} -4.03747i q^{34} +(-1.40056 - 3.84682i) q^{35} +(-0.620123 - 1.07408i) q^{36} +5.80975i q^{37} +(0.255807 + 0.443071i) q^{38} +(-0.588380 + 3.55722i) q^{39} +(2.18508 - 3.78467i) q^{40} +(-1.60485 + 0.926561i) q^{41} +(0.788959 + 2.16698i) q^{42} +(3.93747 - 6.81990i) q^{43} +(3.88384 + 2.24233i) q^{44} -1.54733i q^{45} +1.99189i q^{46} +(2.10152 + 1.21331i) q^{47} +(0.00935211 - 0.0161983i) q^{48} +(1.21689 + 6.89342i) q^{49} +(-1.96699 + 1.13565i) q^{50} +(2.31602 - 4.01147i) q^{51} +(-4.18562 + 1.57394i) q^{52} +(6.49352 + 11.2471i) q^{53} +0.871638i q^{54} +(2.79753 + 4.84547i) q^{55} +(-4.80264 + 5.72471i) q^{56} +0.586956i q^{57} +(1.62380 - 0.937502i) q^{58} +5.41501i q^{59} +(1.66196 - 0.959535i) q^{60} +(4.85421 + 8.40774i) q^{61} +(4.52782 + 7.84241i) q^{62} +(-0.459174 + 2.60560i) q^{63} -4.90038 q^{64} +(-5.50419 - 0.910418i) q^{65} +(-1.57590 - 2.72954i) q^{66} +(-1.66329 - 0.960298i) q^{67} +5.74488 q^{68} +(-1.14261 + 1.97906i) q^{69} +(-3.35304 + 1.22078i) q^{70} +(-9.14766 - 5.28141i) q^{71} +(-2.44594 + 1.41216i) q^{72} +(-1.96780 + 1.13611i) q^{73} +5.06400 q^{74} -2.60577 q^{75} +(-0.630441 + 0.363985i) q^{76} +(-3.27296 - 8.98963i) q^{77} +(3.10061 + 0.512855i) q^{78} +(5.78378 - 10.0178i) q^{79} +(0.0250642 + 0.0144708i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.807626 + 1.39885i) q^{82} -9.45200i q^{83} +(-3.08338 + 1.12260i) q^{84} +(6.20707 + 3.58365i) q^{85} +(-5.94449 - 3.43205i) q^{86} +2.15113 q^{87} +(5.10631 - 8.84438i) q^{88} +12.6671i q^{89} -1.34871 q^{90} +(8.99853 + 3.16647i) q^{91} -2.83424 q^{92} +10.3892i q^{93} +(1.05757 - 1.83177i) q^{94} -0.908215 q^{95} +(-4.90599 - 2.83247i) q^{96} +(-14.3826 - 8.30380i) q^{97} +(6.00857 - 1.06069i) q^{98} -3.61595i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9	$ 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9} + 2 q^{10} - 12 q^{11} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} + 42 q^{16} + 16 q^{17} + 3 q^{18} - 9 q^{19} - 5 q^{21} - 9 q^{22} - 36 q^{23} + 3 q^{24} + 12 q^{25} - 16 q^{26} - 20 q^{27} - 2 q^{28} - 3 q^{29} - 2 q^{30} - 18 q^{31} - 12 q^{33} + 18 q^{35} + 13 q^{36} + 9 q^{38} + 7 q^{39} + 5 q^{40} + 21 q^{41} + 16 q^{42} + 16 q^{43} - 6 q^{44} + 21 q^{47} + 21 q^{48} - 24 q^{49} - 54 q^{50} + 8 q^{51} - 41 q^{52} - 26 q^{53} + 17 q^{55} - 6 q^{56} + 42 q^{58} + 4 q^{62} - 7 q^{63} - 46 q^{64} - 50 q^{65} + 9 q^{66} - 3 q^{67} + 6 q^{68} - 18 q^{69} + 15 q^{71} + 3 q^{72} - 9 q^{73} + 12 q^{74} + 24 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} - 24 q^{80} - 10 q^{81} + 15 q^{82} + 41 q^{84} - 78 q^{85} + 3 q^{86} - 6 q^{87} - 22 q^{88} - 4 q^{90} + 4 q^{91} + 142 q^{92} + 36 q^{94} - 84 q^{95} - 24 q^{96} - 15 q^{97} + 81 q^{98}+O(q^{100}) $ 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9 + 2 * q^10 - 12 * q^11 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 + 42 * q^16 + 16 * q^17 + 3 * q^18 - 9 * q^19 - 5 * q^21 - 9 * q^22 - 36 * q^23 + 3 * q^24 + 12 * q^25 - 16 * q^26 - 20 * q^27 - 2 * q^28 - 3 * q^29 - 2 * q^30 - 18 * q^31 - 12 * q^33 + 18 * q^35 + 13 * q^36 + 9 * q^38 + 7 * q^39 + 5 * q^40 + 21 * q^41 + 16 * q^42 + 16 * q^43 - 6 * q^44 + 21 * q^47 + 21 * q^48 - 24 * q^49 - 54 * q^50 + 8 * q^51 - 41 * q^52 - 26 * q^53 + 17 * q^55 - 6 * q^56 + 42 * q^58 + 4 * q^62 - 7 * q^63 - 46 * q^64 - 50 * q^65 + 9 * q^66 - 3 * q^67 + 6 * q^68 - 18 * q^69 + 15 * q^71 + 3 * q^72 - 9 * q^73 + 12 * q^74 + 24 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 - 24 * q^80 - 10 * q^81 + 15 * q^82 + 41 * q^84 - 78 * q^85 + 3 * q^86 - 6 * q^87 - 22 * q^88 - 4 * q^90 + 4 * q^91 + 142 * q^92 + 36 * q^94 - 84 * q^95 - 24 * q^96 - 15 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	0.871638i		−	0.616341i	−0.951331	−	0.308171i	$-0.900283\pi$
$2$		−	0.871638i		−	0.616341i	0.951331	−	0.308171i	$-0.0997168\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	1.24025			0.620123
$5$	1.34003	+	0.773665i	0.599278	+	0.345993i	0.768758	−	0.639540i	$-0.220875\pi$
$5$	1.34003	+	0.773665i	0.599278	+	0.345993i	−0.169479	+	0.985534i	$0.554209\pi$
$6$	−0.754861	−	0.435819i	−0.308171	−	0.177922i
$7$	−2.02693	−	1.70046i	−0.766108	−	0.642712i
$7$	−2.02693	−	1.70046i	−0.766108	−	0.642712i
$8$		−	2.82432i		−	0.998549i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.674356	−	1.16802i	0.213250	−	0.369360i
$11$	3.13150	+	1.80798i	0.944184	+	0.545125i	0.891270	−	0.453474i	$-0.149816\pi$
$11$	3.13150	+	1.80798i	0.944184	+	0.545125i	0.0529148	+	0.998599i	$0.483149\pi$
$12$	0.620123	−	1.07408i	0.179014	−	0.310062i
$13$	−3.37483	+	1.26906i	−0.936010	+	0.351973i
$13$	−3.37483	+	1.26906i	−0.936010	+	0.351973i
$14$	−1.48218	+	1.76675i	−0.396130	+	0.472184i
$15$	1.34003	−	0.773665i	0.345993	−	0.199759i
$16$	0.0187042			0.00467605
$17$	4.63205			1.12344			0.561718	−	0.827329i	$-0.310141\pi$
$17$	4.63205			1.12344			0.561718	+	0.827329i	$0.310141\pi$
$18$	−0.754861	+	0.435819i	−0.177922	+	0.102724i
$19$	−0.508319	+	0.293478i	−0.116616	+	0.0673285i	−0.557174	−	0.830396i	$-0.688114\pi$
$19$	−0.508319	+	0.293478i	−0.116616	+	0.0673285i	0.440557	+	0.897725i	$0.354781\pi$
$20$	1.66196	+	0.959535i	0.371626	+	0.214559i
$21$	−2.48610	+	0.905145i	−0.542512	+	0.197519i
$22$	1.57590	−	2.72954i	0.335983	−	0.581940i
$23$	−2.28523			−0.476503			−0.238251	−	0.971204i	$-0.576574\pi$
$23$	−2.28523			−0.476503			−0.238251	+	0.971204i	$0.576574\pi$
$24$	−2.44594	−	1.41216i	−0.499275	−	0.288256i
$25$	−1.30289	−	2.25666i	−0.260577	−	0.451333i
$26$	1.10616	+	2.94163i	0.216936	+	0.576902i
$27$	−1.00000			−0.192450
$28$	−2.51389	−	2.10899i	−0.475081	−	0.398561i
$29$	1.07556	+	1.86293i	0.199727	+	0.345937i	0.948440	−	0.316957i	$-0.102661\pi$
$29$	1.07556	+	1.86293i	0.199727	+	0.345937i	−0.748713	+	0.662894i	$0.769328\pi$
$30$	−0.674356	−	1.16802i	−0.123120	−	0.213250i
$31$	−8.99732	+	5.19461i	−1.61597	+	0.932979i	−0.628018	+	0.778199i	$0.716134\pi$
$31$	−8.99732	+	5.19461i	−1.61597	+	0.932979i	−0.987949	+	0.154781i	$0.950533\pi$
$32$		−	5.66495i		−	1.00143i
$33$	3.13150	−	1.80798i	0.545125	−	0.314728i
$34$		−	4.03747i		−	0.692420i
$35$	−1.40056	−	3.84682i	−0.236737	−	0.650232i
$36$	−0.620123	−	1.07408i	−0.103354	−	0.179014i
$37$			5.80975i			0.955116i	0.878600	+	0.477558i	$0.158478\pi$
$37$			5.80975i			0.955116i	−0.878600	+	0.477558i	$0.841522\pi$
$38$	0.255807	+	0.443071i	0.0414974	+	0.0718755i
$39$	−0.588380	+	3.55722i	−0.0942162	+	0.569611i
$40$	2.18508	−	3.78467i	0.345491	−	0.598409i
$41$	−1.60485	+	0.926561i	−0.250636	+	0.144704i	−0.620055	−	0.784558i	$-0.712890\pi$
$41$	−1.60485	+	0.926561i	−0.250636	+	0.144704i	0.369420	+	0.929263i	$0.379556\pi$
$42$	0.788959	+	2.16698i	0.121739	+	0.334373i
$43$	3.93747	−	6.81990i	0.600459	−	1.04003i	−0.392293	−	0.919840i	$-0.628318\pi$
$43$	3.93747	−	6.81990i	0.600459	−	1.04003i	0.992752	−	0.120185i	$-0.0383487\pi$
$44$	3.88384	+	2.24233i	0.585511	+	0.338045i
$45$		−	1.54733i		−	0.230662i
$46$			1.99189i			0.293688i
$47$	2.10152	+	1.21331i	0.306538	+	0.176980i	0.645376	−	0.763865i	$-0.276701\pi$
$47$	2.10152	+	1.21331i	0.306538	+	0.176980i	−0.338838	+	0.940845i	$0.610034\pi$
$48$	0.00935211	−	0.0161983i	0.00134986	−	0.00233803i
$49$	1.21689	+	6.89342i	0.173842	+	0.984774i
$50$	−1.96699	+	1.13565i	−0.278175	+	0.160604i
$51$	2.31602	−	4.01147i	0.324308	−	0.561718i
$52$	−4.18562	+	1.57394i	−0.580442	+	0.218267i
$53$	6.49352	+	11.2471i	0.891954	+	1.54491i	0.837530	+	0.546391i	$0.183999\pi$
$53$	6.49352	+	11.2471i	0.891954	+	1.54491i	0.0544233	+	0.998518i	$0.482668\pi$
$54$			0.871638i			0.118615i
$55$	2.79753	+	4.84547i	0.377219	+	0.653363i
$56$	−4.80264	+	5.72471i	−0.641780	+	0.764996i
$57$			0.586956i			0.0777443i
$58$	1.62380	−	0.937502i	0.213216	−	0.123100i
$59$			5.41501i			0.704975i	0.935817	+	0.352487i	$0.114664\pi$
$59$			5.41501i			0.704975i	−0.935817	+	0.352487i	$0.885336\pi$
$60$	1.66196	−	0.959535i	0.214559	−	0.123875i
$61$	4.85421	+	8.40774i	0.621518	+	1.07650i	0.989203	+	0.146550i	$0.0468170\pi$
$61$	4.85421	+	8.40774i	0.621518	+	1.07650i	−0.367685	+	0.929950i	$0.619850\pi$
$62$	4.52782	+	7.84241i	0.575034	+	0.995988i
$63$	−0.459174	+	2.60560i	−0.0578504	+	0.328275i
$64$	−4.90038			−0.612547
$65$	−5.50419	−	0.910418i	−0.682711	−	0.112923i
$66$	−1.57590	−	2.72954i	−0.193980	−	0.335983i
$67$	−1.66329	−	0.960298i	−0.203203	−	0.117319i	0.394946	−	0.918704i	$-0.370763\pi$
$67$	−1.66329	−	0.960298i	−0.203203	−	0.117319i	−0.598148	+	0.801385i	$0.704097\pi$
$68$	5.74488			0.696669
$69$	−1.14261	+	1.97906i	−0.137554	+	0.238251i
$70$	−3.35304	+	1.22078i	−0.400765	+	0.145911i
$71$	−9.14766	−	5.28141i	−1.08563	−	0.626788i	−0.153219	−	0.988192i	$-0.548964\pi$
$71$	−9.14766	−	5.28141i	−1.08563	−	0.626788i	−0.932409	+	0.361405i	$0.882297\pi$
$72$	−2.44594	+	1.41216i	−0.288256	+	0.166425i
$73$	−1.96780	+	1.13611i	−0.230313	+	0.132971i	−0.610717	−	0.791849i	$-0.709118\pi$
$73$	−1.96780	+	1.13611i	−0.230313	+	0.132971i	0.380403	+	0.924821i	$0.375785\pi$
$74$	5.06400			0.588678
$75$	−2.60577			−0.300889
$76$	−0.630441	+	0.363985i	−0.0723165	+	0.0417520i
$77$	−3.27296	−	8.98963i	−0.372988	−	1.02446i
$78$	3.10061	+	0.512855i	0.351075	+	0.0580694i
$79$	5.78378	−	10.0178i	0.650726	−	1.12709i	−0.332221	−	0.943202i	$-0.607798\pi$
$79$	5.78378	−	10.0178i	0.650726	−	1.12709i	0.982947	−	0.183889i	$-0.0588686\pi$
$80$	0.0250642	+	0.0144708i	0.00280226	+	0.00161788i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.807626	+	1.39885i	0.0891874	+	0.154477i
$83$		−	9.45200i		−	1.03749i	−0.854928	−	0.518746i	$-0.826399\pi$
$83$		−	9.45200i		−	1.03749i	0.854928	−	0.518746i	$-0.173601\pi$
$84$	−3.08338	+	1.12260i	−0.336425	+	0.122486i
$85$	6.20707	+	3.58365i	0.673251	+	0.388702i
$86$	−5.94449	−	3.43205i	−0.641011	−	0.370088i
$87$	2.15113			0.230625
$88$	5.10631	−	8.84438i	0.544334	−	0.942814i
$89$			12.6671i			1.34272i	0.741134	+	0.671358i	$0.234288\pi$
$89$			12.6671i			1.34272i	−0.741134	+	0.671358i	$0.765712\pi$
$90$	−1.34871			−0.142167
$91$	8.99853	+	3.16647i	0.943302	+	0.331936i
$92$	−2.83424			−0.295490
$93$			10.3892i			1.07731i
$94$	1.05757	−	1.83177i	0.109080	−	0.188932i
$95$	−0.908215			−0.0931809
$96$	−4.90599	−	2.83247i	−0.500716	−	0.289088i
$97$	−14.3826	−	8.30380i	−1.46033	−	0.843124i	−0.461307	−	0.887241i	$-0.652619\pi$
$97$	−14.3826	−	8.30380i	−1.46033	−	0.843124i	−0.999026	+	0.0441172i	$0.985952\pi$
$98$	6.00857	−	1.06069i	0.606957	−	0.107146i
$99$		−	3.61595i		−	0.363417i
$100$	−1.61590	−	2.79882i	−0.161590	−	0.279882i
$101$	−6.54956	+	11.3442i	−0.651705	+	1.12879i	0.331003	+	0.943630i	$0.392613\pi$
$101$	−6.54956	+	11.3442i	−0.651705	+	1.12879i	−0.982709	+	0.185157i	$0.940721\pi$
$102$	−3.49655	−	2.01873i	−0.346210	−	0.199885i
$103$	−0.0841095	+	0.145682i	−0.00828756	+	0.0143545i	−0.870139	−	0.492806i	$-0.835971\pi$
$103$	−0.0841095	+	0.145682i	−0.00828756	+	0.0143545i	0.861852	+	0.507160i	$0.169305\pi$
$104$	3.58423	+	9.53162i	0.351463	+	0.934652i
$105$	−4.03172	−	0.710493i	−0.393456	−	0.0693370i
$106$	9.80341	−	5.66000i	0.952191	−	0.549748i
$107$	−1.58262			−0.152998			−0.0764990	−	0.997070i	$-0.524374\pi$
$107$	−1.58262			−0.152998			−0.0764990	+	0.997070i	$0.524374\pi$
$108$	−1.24025			−0.119343
$109$	3.76860	−	2.17580i	0.360966	−	0.208404i	−0.308538	−	0.951212i	$-0.599840\pi$
$109$	3.76860	−	2.17580i	0.360966	−	0.208404i	0.669504	+	0.742808i	$0.266506\pi$
$110$	4.22350	−	2.43844i	0.402695	−	0.232496i
$111$	5.03139	+	2.90487i	0.477558	+	0.275718i
$112$	−0.0379121	−	0.0318057i	−0.00358236	−	0.00300536i
$113$	6.62266	−	11.4708i	0.623007	−	1.07908i	−0.365915	−	0.930648i	$-0.619244\pi$
$113$	6.62266	−	11.4708i	0.623007	−	1.07908i	0.988923	−	0.148432i	$-0.0474226\pi$
$114$	0.511614			0.0479170
$115$	−3.06226	−	1.76800i	−0.285558	−	0.164867i
$116$	1.33396	+	2.31049i	0.123855	+	0.214524i
$117$	2.78645	+	2.28816i	0.257608	+	0.211541i
$118$	4.71993			0.434505
$119$	−9.38883	−	7.87659i	−0.860673	−	0.722046i
$120$	−2.18508	−	3.78467i	−0.199470	−	0.345491i
$121$	1.03755	+	1.79709i	0.0943226	+	0.163372i
$122$	7.32851	−	4.23111i	0.663492	−	0.383067i
$123$			1.85312i			0.167090i
$124$	−11.1589	+	6.44259i	−1.00210	+	0.578562i
$125$		−	11.7686i		−	1.05262i
$126$	2.27114	+	0.400233i	0.202329	+	0.0356556i
$127$	1.74707	+	3.02602i	0.155028	+	0.268516i	0.933069	−	0.359697i	$-0.117120\pi$
$127$	1.74707	+	3.02602i	0.155028	+	0.268516i	−0.778041	+	0.628213i	$0.783787\pi$
$128$		−	7.05854i		−	0.623893i
$129$	−3.93747	−	6.81990i	−0.346675	−	0.600459i
$130$	−0.793555	+	4.79766i	−0.0695994	+	0.420783i
$131$	−3.04778	+	5.27892i	−0.266286	+	0.461221i	−0.967900	−	0.251336i	$-0.919130\pi$
$131$	−3.04778	+	5.27892i	−0.266286	+	0.461221i	0.701614	+	0.712558i	$0.252463\pi$
$132$	3.88384	−	2.24233i	0.338045	−	0.195170i
$133$	1.52937	+	0.269515i	0.132614	+	0.0233699i
$134$	−0.837033	+	1.44978i	−0.0723086	+	0.125242i
$135$	−1.34003	−	0.773665i	−0.115331	−	0.0665865i
$136$		−	13.0824i		−	1.12181i
$137$		−	2.47086i		−	0.211099i	−0.994414	−	0.105550i	$-0.966340\pi$
$137$		−	2.47086i		−	0.211099i	0.994414	−	0.105550i	$-0.0336602\pi$
$138$	1.72503	+	0.995945i	0.146844	+	0.0847805i
$139$	5.27760	−	9.14107i	0.447640	−	0.775335i	−0.550592	−	0.834775i	$-0.685598\pi$
$139$	5.27760	−	9.14107i	0.447640	−	0.775335i	0.998232	+	0.0594393i	$0.0189313\pi$
$140$	−1.73704	−	4.77101i	−0.146806	−	0.403224i
$141$	2.10152	−	1.21331i	0.176980	−	0.102179i
$142$	−4.60348	+	7.97346i	−0.386315	+	0.669118i
$143$	−12.8627	−	2.12755i	−1.07564	−	0.177915i
$144$	−0.00935211	−	0.0161983i	−0.000779342	−	0.00134986i
$145$			3.32850i			0.276417i
$146$	0.990275	+	1.71521i	0.0819558	+	0.141952i
$147$	6.57832	+	2.39285i	0.542571	+	0.197359i
$148$			7.20552i			0.592290i
$149$	10.4409	−	6.02804i	0.855350	−	0.493836i	−0.00710248	−	0.999975i	$-0.502261\pi$
$149$	10.4409	−	6.02804i	0.855350	−	0.493836i	0.862452	+	0.506138i	$0.168927\pi$
$150$			2.27129i			0.185450i
$151$	5.84616	−	3.37528i	0.475754	−	0.274677i	−0.242891	−	0.970053i	$-0.578096\pi$
$151$	5.84616	−	3.37528i	0.475754	−	0.274677i	0.718645	+	0.695377i	$0.244763\pi$
$152$	0.828877	+	1.43566i	0.0672308	+	0.116447i
$153$	−2.31602	−	4.01147i	−0.187239	−	0.324308i
$154$	−7.83571	+	2.85284i	−0.631419	+	0.229888i
$155$	−16.0755			−1.29122
$156$	−0.729736	+	4.41183i	−0.0584257	+	0.353229i
$157$	−1.42832	−	2.47392i	−0.113992	−	0.197441i	0.803384	−	0.595461i	$-0.203031\pi$
$157$	−1.42832	−	2.47392i	−0.113992	−	0.197441i	−0.917376	+	0.398021i	$0.869697\pi$
$158$	−8.73190	−	5.04136i	−0.694673	−	0.401069i
$159$	12.9870			1.02994
$160$	4.38277	−	7.59118i	0.346489	−	0.600136i
$161$	4.63199	+	3.88593i	0.365052	+	0.306254i
$162$	0.754861	+	0.435819i	0.0593075	+	0.0342412i
$163$	−14.8902	+	8.59686i	−1.16629	+	0.673358i	−0.952804	−	0.303588i	$-0.901816\pi$
$163$	−14.8902	+	8.59686i	−1.16629	+	0.673358i	−0.213487	+	0.976946i	$0.568482\pi$
$164$	−1.99041	+	1.14916i	−0.155425	+	0.0897346i
$165$	5.59507			0.435575
$166$	−8.23873			−0.639449
$167$	11.8526	−	6.84312i	0.917185	−	0.529537i	0.0344489	−	0.999406i	$-0.489032\pi$
$167$	11.8526	−	6.84312i	0.917185	−	0.529537i	0.882736	+	0.469870i	$0.155699\pi$
$168$	2.55642	+	7.02156i	0.197232	+	0.541725i
$169$	9.77899	−	8.56571i	0.752230	−	0.658901i
$170$	3.12365	−	5.41032i	0.239573	−	0.414952i
$171$	0.508319	+	0.293478i	0.0388721	+	0.0224428i
$172$	4.88343	−	8.45836i	0.372358	−	0.644944i
$173$	−9.15726	−	15.8608i	−0.696214	−	1.20588i	−0.969770	−	0.244022i	$-0.921533\pi$
$173$	−9.15726	−	15.8608i	−0.696214	−	1.20588i	0.273556	−	0.961856i	$-0.411800\pi$
$174$		−	1.87500i		−	0.142144i
$175$	−1.19650	+	6.78960i	−0.0904470	+	0.513246i
$176$	0.0585724	+	0.0338168i	0.00441506	+	0.00254903i
$177$	4.68954	+	2.70751i	0.352487	+	0.203509i
$178$	11.0412			0.827571
$179$	9.18131	−	15.9025i	0.686243	−	1.18861i	−0.286801	−	0.957990i	$-0.592592\pi$
$179$	9.18131	−	15.9025i	0.686243	−	1.18861i	0.973044	−	0.230618i	$-0.0740748\pi$
$180$		−	1.91907i		−	0.143039i
$181$	−18.0249			−1.33978			−0.669889	−	0.742462i	$-0.733658\pi$
$181$	−18.0249			−1.33978			−0.669889	+	0.742462i	$0.733658\pi$
$182$	2.76001	−	7.84346i	0.204586	−	0.581396i
$183$	9.70842			0.717667
$184$			6.45422i			0.475811i
$185$	−4.49480	+	7.78521i	−0.330464	+	0.572380i
$186$	9.05564			0.663992
$187$	14.5053	+	8.37462i	1.06073	+	0.612413i
$188$	2.60640	+	1.50481i	0.190092	+	0.109749i
$189$	2.02693	+	1.70046i	0.147437	+	0.123690i
$190$			0.791635i			0.0574313i
$191$	−12.1990	−	21.1293i	−0.882691	−	1.52887i	−0.848338	−	0.529456i	$-0.822396\pi$
$191$	−12.1990	−	21.1293i	−0.882691	−	1.52887i	−0.0343532	−	0.999410i	$-0.510937\pi$
$192$	−2.45019	+	4.24385i	−0.176827	+	0.306274i
$193$	−10.4054	−	6.00758i	−0.748999	−	0.432435i	0.0763329	−	0.997082i	$-0.475679\pi$
$193$	−10.4054	−	6.00758i	−0.748999	−	0.432435i	−0.825332	+	0.564647i	$0.809012\pi$
$194$	−7.23792	+	12.5364i	−0.519652	+	0.900064i
$195$	−3.54054	+	4.31156i	−0.253543	+	0.308757i
$196$	1.50925	+	8.54953i	0.107803	+	0.610681i
$197$	−18.2189	+	10.5187i	−1.29804	+	0.749424i	−0.980065	−	0.198675i	$-0.936336\pi$
$197$	−18.2189	+	10.5187i	−1.29804	+	0.749424i	−0.317975	+	0.948099i	$0.603003\pi$
$198$	−3.15180			−0.223989
$199$	1.08768			0.0771034			0.0385517	−	0.999257i	$-0.487726\pi$
$199$	1.08768			0.0771034			0.0385517	+	0.999257i	$0.487726\pi$
$200$	−6.37355	+	3.67977i	−0.450678	+	0.260199i
$201$	−1.66329	+	0.960298i	−0.117319	+	0.0677342i
$202$	9.88801	+	5.70885i	0.695718	+	0.401673i
$203$	0.987740	−	5.60498i	0.0693258	−	0.393392i
$204$	2.87244	−	4.97521i	0.201111	−	0.348334i
$205$	−2.86739			−0.200267
$206$	0.126982	+	0.0733131i	0.00884725	+	0.00510796i
$207$	1.14261	+	1.97906i	0.0794171	+	0.137554i
$208$	−0.0631236	+	0.0237367i	−0.00437683	+	0.00164585i
$209$	−2.12241			−0.146810
$210$	−0.619293	+	3.51421i	−0.0427353	+	0.242503i
$211$	10.2015	+	17.6694i	0.702297	+	1.21641i	0.967658	+	0.252266i	$0.0811757\pi$
$211$	10.2015	+	17.6694i	0.702297	+	1.21641i	−0.265361	+	0.964149i	$0.585491\pi$
$212$	8.05357	+	13.9492i	0.553121	+	0.958034i
$213$	−9.14766	+	5.28141i	−0.626788	+	0.361876i
$214$			1.37948i			0.0942990i
$215$	10.5526	−	6.09257i	0.719684	−	0.415510i
$216$			2.82432i			0.192171i
$217$	27.0702	+	4.77045i	1.83764	+	0.323839i
$218$	−1.89651	−	3.28485i	−0.128448	−	0.222478i
$219$			2.27222i			0.153542i
$220$	3.46963	+	6.00958i	0.233922	+	0.405166i
$221$	−15.6324	+	5.87833i	−1.05155	+	0.395419i
$222$	2.53200	−	4.38555i	0.169937	−	0.294339i
$223$	−9.56277	+	5.52107i	−0.640371	+	0.369718i	−0.784757	−	0.619803i	$-0.787212\pi$
$223$	−9.56277	+	5.52107i	−0.640371	+	0.369718i	0.144387	+	0.989521i	$0.453879\pi$
$224$	−9.63300	+	11.4825i	−0.643632	+	0.767204i
$225$	−1.30289	+	2.25666i	−0.0868590	+	0.150444i
$226$	−9.99837	−	5.77256i	−0.665082	−	0.383985i
$227$		−	12.1047i		−	0.803417i	−0.915767	−	0.401709i	$-0.868416\pi$
$227$		−	12.1047i		−	0.803417i	0.915767	−	0.401709i	$-0.131584\pi$
$228$			0.727971i			0.0482110i
$229$	12.4222	+	7.17199i	0.820885	+	0.473938i	0.850722	−	0.525617i	$-0.176165\pi$
$229$	12.4222	+	7.17199i	0.820885	+	0.473938i	−0.0298364	+	0.999555i	$0.509499\pi$
$230$	−1.54106	+	2.66919i	−0.101614	+	0.176001i
$231$	−9.42173	−	1.66035i	−0.619904	−	0.109243i
$232$	5.26152	−	3.03774i	0.345435	−	0.199437i
$233$	10.5498	−	18.2727i	0.691137	−	1.19709i	−0.280328	−	0.959904i	$-0.590443\pi$
$233$	10.5498	−	18.2727i	0.691137	−	1.19709i	0.971465	−	0.237181i	$-0.0762234\pi$
$234$	1.99445	−	2.42878i	0.130381	−	0.158774i
$235$	1.87740	+	3.25175i	0.122468	+	0.212120i
$236$			6.71595i			0.437171i
$237$	−5.78378	−	10.0178i	−0.375697	−	0.650726i
$238$	−6.86554	+	8.18367i	−0.445027	+	0.530468i
$239$			4.64324i			0.300346i	0.988660	+	0.150173i	$0.0479831\pi$
$239$			4.64324i			0.300346i	−0.988660	+	0.150173i	$0.952017\pi$
$240$	0.0250642	−	0.0144708i	0.00161788	−	0.000934086i
$241$		−	8.03989i		−	0.517895i	−0.965891	−	0.258948i	$-0.916624\pi$
$241$		−	8.03989i		−	0.517895i	0.965891	−	0.258948i	$-0.0833757\pi$
$242$	1.56641	−	0.904367i	0.100693	−	0.0581349i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	6.02042	+	10.4277i	0.385418	+	0.667563i
$245$	−3.70252	+	10.1788i	−0.236546	+	0.650301i
$246$	1.61525			0.102985
$247$	1.34305	−	1.63553i	0.0854563	−	0.104066i
$248$	14.6713	+	25.4114i	0.931625	+	1.61362i
$249$	−8.18567	−	4.72600i	−0.518746	−	0.299498i
$250$	−10.2580			−0.648773
$251$	6.22683	−	10.7852i	0.393034	−	0.680755i	−0.599814	−	0.800140i	$-0.704759\pi$
$251$	6.22683	−	10.7852i	0.393034	−	0.680755i	0.992848	+	0.119384i	$0.0380921\pi$
$252$	−0.569488	+	3.23159i	−0.0358744	+	0.203571i
$253$	−7.15620	−	4.13163i	−0.449906	−	0.259753i
$254$	2.63760	−	1.52282i	0.165498	−	0.0955501i
$255$	6.20707	−	3.58365i	0.388702	−	0.224417i
$256$	−15.9533			−0.997078
$257$	7.17256			0.447412			0.223706	−	0.974657i	$-0.428185\pi$
$257$	7.17256			0.447412			0.223706	+	0.974657i	$0.428185\pi$
$258$	−5.94449	+	3.43205i	−0.370088	+	0.213670i
$259$	9.87922	−	11.7759i	0.613865	−	0.731722i
$260$	−6.82655	−	1.12914i	−0.423365	−	0.0700265i
$261$	1.07556	−	1.86293i	0.0665757	−	0.115312i
$262$	4.60131	+	2.65657i	0.284270	+	0.164123i
$263$	−8.67804	+	15.0308i	−0.535111	+	0.926839i	0.464047	+	0.885810i	$0.346397\pi$
$263$	−8.67804	+	15.0308i	−0.535111	+	0.926839i	−0.999158	+	0.0410286i	$0.986937\pi$
$264$	−5.10631	−	8.84438i	−0.314271	−	0.544334i
$265$			20.0952i			1.23444i
$266$	0.234920	−	1.33306i	0.0144038	−	0.0817353i
$267$	10.9701	+	6.33357i	0.671358	+	0.387608i
$268$	−2.06288	−	1.19101i	−0.126011	−	0.0727523i
$269$	11.2092			0.683435			0.341717	−	0.939803i	$-0.388991\pi$
$269$	11.2092			0.683435			0.341717	+	0.939803i	$0.388991\pi$
$270$	−0.674356	+	1.16802i	−0.0410400	+	0.0710834i
$271$		−	25.6318i		−	1.55702i	−0.627632	−	0.778510i	$-0.715976\pi$
$271$		−	25.6318i		−	1.55702i	0.627632	−	0.778510i	$-0.284024\pi$
$272$	0.0866388			0.00525325
$273$	7.24150	−	6.20972i	0.438276	−	0.375829i
$274$	−2.15369			−0.130109
$275$		−	9.42234i		−	0.568188i
$276$	−1.41712	+	2.45453i	−0.0853007	+	0.147745i
$277$	−12.4061			−0.745413			−0.372706	−	0.927949i	$-0.621570\pi$
$277$	−12.4061			−0.745413			−0.372706	+	0.927949i	$0.621570\pi$
$278$	−7.96771	−	4.60016i	−0.477871	−	0.275899i
$279$	8.99732	+	5.19461i	0.538656	+	0.310993i
$280$	−10.8647	+	3.95563i	−0.649288	+	0.236394i
$281$			30.8640i			1.84119i	0.390513	+	0.920597i	$0.372298\pi$
$281$			30.8640i			1.84119i	−0.390513	+	0.920597i	$0.627702\pi$
$282$	−1.05757	−	1.83177i	−0.0629774	−	0.109080i
$283$	−5.36758	+	9.29692i	−0.319069	+	0.552644i	−0.980294	−	0.197543i	$-0.936704\pi$
$283$	−5.36758	+	9.29692i	−0.319069	+	0.552644i	0.661225	+	0.750188i	$0.270037\pi$
$284$	−11.3454	−	6.55025i	−0.673223	−	0.388686i
$285$	−0.454108	+	0.786537i	−0.0268990	+	0.0465905i
$286$	−1.85446	+	11.2116i	−0.109656	+	0.662959i
$287$	4.82850	+	0.850905i	0.285017	+	0.0502273i
$288$	−4.90599	+	2.83247i	−0.289088	+	0.166905i
$289$	4.45585			0.262109
$290$	2.90125			0.170367
$291$	−14.3826	+	8.30380i	−0.843124	+	0.486778i
$292$	−2.44055	+	1.40905i	−0.142823	+	0.0824586i
$293$	−0.0137087	−	0.00791474i	−0.000800872	−	0.000462384i	0.499600	−	0.866257i	$-0.333481\pi$
$293$	−0.0137087	−	0.00791474i	−0.000800872	−	0.000462384i	−0.500400	+	0.865794i	$0.666814\pi$
$294$	2.08570	−	5.73392i	0.121640	−	0.334409i
$295$	−4.18941	+	7.25626i	−0.243917	+	0.422476i
$296$	16.4086			0.953730
$297$	−3.13150	−	1.80798i	−0.181708	−	0.104909i
$298$	−5.25427	−	9.10067i	−0.304372	−	0.527188i
$299$	7.71225	−	2.90008i	0.446011	−	0.167716i
$300$	−3.23180			−0.186588
$301$	−19.5779	+	7.12796i	−1.12845	+	0.410849i
$302$	−2.94203	−	5.09574i	−0.169295	−	0.293227i
$303$	6.54956	+	11.3442i	0.376262	+	0.651705i
$304$	−0.00950771	+	0.00548928i	−0.000545305	+	0.000314832i
$305$			15.0221i			0.860164i
$306$	−3.49655	+	2.01873i	−0.199885	+	0.115403i
$307$		−	22.7982i		−	1.30116i	−0.759437	−	0.650581i	$-0.774526\pi$
$307$		−	22.7982i		−	1.30116i	0.759437	−	0.650581i	$-0.225474\pi$
$308$	−4.05928	−	11.1494i	−0.231299	−	0.635293i
$309$	0.0841095	+	0.145682i	0.00478482	+	0.00828756i
$310$			14.0121i			0.795831i
$311$	1.79592	+	3.11062i	0.101837	+	0.176387i	0.912442	−	0.409207i	$-0.134195\pi$
$311$	1.79592	+	3.11062i	0.101837	+	0.176387i	−0.810604	+	0.585594i	$0.800861\pi$
$312$	10.0467	+	1.66178i	0.568784	+	0.0940795i
$313$	4.08399	−	7.07368i	0.230841	−	0.399828i	−0.727215	−	0.686410i	$-0.759186\pi$
$313$	4.08399	−	7.07368i	0.230841	−	0.399828i	0.958056	+	0.286582i	$0.0925190\pi$
$314$	−2.15637	+	1.24498i	−0.121691	+	0.0702582i
$315$	−2.63117	+	3.13633i	−0.148249	+	0.176712i
$316$	7.17331	−	12.4245i	0.403530	−	0.698935i
$317$	19.6172	+	11.3260i	1.10181	+	0.636131i	0.936696	−	0.350143i	$-0.113867\pi$
$317$	19.6172	+	11.3260i	1.10181	+	0.636131i	0.165116	+	0.986274i	$0.447200\pi$
$318$		−	11.3200i		−	0.634794i
$319$			7.77836i			0.435505i
$320$	−6.56664	−	3.79125i	−0.367086	−	0.211937i
$321$	−0.791312	+	1.37059i	−0.0441667	+	0.0764990i
$322$	3.38712	−	4.03742i	0.188757	−	0.224997i
$323$	−2.35456	+	1.35940i	−0.131011	+	0.0756393i
$324$	−0.620123	+	1.07408i	−0.0344513	+	0.0596714i
$325$	7.26086	+	5.96243i	0.402760	+	0.330736i
$326$	7.49336	+	12.9789i	0.415019	+	0.718833i
$327$		−	4.35160i		−	0.240644i
$328$	2.61691	+	4.53262i	0.144495	+	0.250272i
$329$	−2.19645	−	6.03285i	−0.121094	−	0.332602i
$330$		−	4.87688i		−	0.268463i
$331$	−15.5467	+	8.97589i	−0.854524	+	0.493360i	−0.862175	−	0.506611i	$-0.830898\pi$
$331$	−15.5467	+	8.97589i	−0.854524	+	0.493360i	0.00765059	+	0.999971i	$0.497565\pi$
$332$		−	11.7228i		−	0.643373i
$333$	5.03139	−	2.90487i	0.275718	−	0.159186i
$334$	−5.96473	−	10.3312i	−0.326376	−	0.565299i
$335$	−1.48590	−	2.57365i	−0.0811833	−	0.140614i
$336$	−0.0465006	+	0.0169300i	−0.00253682	+	0.000923609i
$337$	−5.23244			−0.285029			−0.142515	−	0.989793i	$-0.545519\pi$
$337$	−5.23244			−0.285029			−0.142515	+	0.989793i	$0.545519\pi$
$338$	−7.46620	−	8.52374i	−0.406108	−	0.463630i
$339$	−6.62266	−	11.4708i	−0.359693	−	0.623007i
$340$	7.69829	+	4.44461i	0.417498	+	0.241043i
$341$	−37.5669			−2.03436
$342$	0.255807	−	0.443071i	0.0138325	−	0.0239585i
$343$	9.25540	−	16.0417i	0.499744	−	0.866173i
$344$	−19.2616	−	11.1207i	−1.03852	−	0.599588i
$345$	−3.06226	+	1.76800i	−0.164867	+	0.0951859i
$346$	−13.8249	+	7.98182i	−0.743232	+	0.429105i
$347$	16.3188			0.876039			0.438019	−	0.898966i	$-0.355680\pi$
$347$	16.3188			0.876039			0.438019	+	0.898966i	$0.355680\pi$
$348$	2.66793			0.143016
$349$	23.6336	−	13.6449i	1.26508	−	0.730394i	0.291027	−	0.956715i	$-0.406003\pi$
$349$	23.6336	−	13.6449i	1.26508	−	0.730394i	0.974053	+	0.226321i	$0.0726698\pi$
$350$	5.91808	+	1.04292i	0.316335	+	0.0557462i
$351$	3.37483	−	1.26906i	0.180135	−	0.0677373i
$352$	10.2421	−	17.7398i	0.545905	−	0.945536i
$353$	24.6048	+	14.2056i	1.30958	+	0.756087i	0.982026	−	0.188745i	$-0.0604419\pi$
$353$	24.6048	+	14.2056i	1.30958	+	0.756087i	0.327555	+	0.944832i	$0.393775\pi$
$354$	2.35997	−	4.08758i	0.125431	−	0.217253i
$355$	−8.17208	−	14.1545i	−0.433729	−	0.751240i
$356$			15.7104i			0.832649i
$357$	−11.5157	+	4.19267i	−0.609478	+	0.221900i
$358$	−13.8612	−	8.00278i	−0.732588	−	0.422960i
$359$	4.79342	+	2.76748i	0.252987	+	0.146062i	0.621131	−	0.783707i	$-0.286673\pi$
$359$	4.79342	+	2.76748i	0.252987	+	0.146062i	−0.368144	+	0.929769i	$0.620007\pi$
$360$	−4.37016			−0.230328
$361$	−9.32774	+	16.1561i	−0.490934	+	0.850322i
$362$			15.7112i			0.825760i
$363$	2.07510			0.108914
$364$	11.1604	+	3.92720i	0.584963	+	0.205841i
$365$	−3.51587			−0.184029
$366$		−	8.46223i		−	0.442328i
$367$	13.2877	−	23.0149i	0.693611	−	1.20137i	−0.277036	−	0.960860i	$-0.589352\pi$
$367$	13.2877	−	23.0149i	0.693611	−	1.20137i	0.970647	−	0.240510i	$-0.0773146\pi$
$368$	−0.0427434			−0.00222815
$369$	1.60485	+	0.926561i	0.0835452	+	0.0482348i
$370$	6.78589	+	3.91784i	0.352782	+	0.203679i
$371$	5.96331	−	33.8391i	0.309599	−	1.75684i
$372$			12.8852i			0.668066i
$373$	8.05846	+	13.9577i	0.417251	+	0.722701i	0.995662	−	0.0930452i	$-0.0296601\pi$
$373$	8.05846	+	13.9577i	0.417251	+	0.722701i	−0.578410	+	0.815746i	$0.696327\pi$
$374$	7.29964	−	12.6434i	0.377456	−	0.653772i
$375$	−10.1919	−	5.88432i	−0.526309	−	0.303865i
$376$	3.42679	−	5.93537i	0.176723	−	0.306094i
$377$	−5.99401	−	4.92212i	−0.308707	−	0.253502i
$378$	1.48218	−	1.76675i	0.0762353	−	0.0908718i
$379$	7.43319	−	4.29156i	0.381817	−	0.220442i	−0.296791	−	0.954942i	$-0.595917\pi$
$379$	7.43319	−	4.29156i	0.381817	−	0.220442i	0.678609	+	0.734500i	$0.262583\pi$
$380$	−1.12641			−0.0577836
$381$	3.49415			0.179011
$382$	−18.4171	+	10.6331i	−0.942303	+	0.544039i
$383$	0.782628	−	0.451851i	0.0399904	−	0.0230885i	−0.479871	−	0.877339i	$-0.659317\pi$
$383$	0.782628	−	0.451851i	0.0399904	−	0.0230885i	0.519862	+	0.854250i	$0.325983\pi$
$384$	−6.11288	−	3.52927i	−0.311946	−	0.180102i
$385$	2.56911	−	14.5785i	0.130934	−	0.742990i
$386$	−5.23644	+	9.06977i	−0.266528	+	0.461639i
$387$	−7.87494			−0.400306
$388$	−17.8380	−	10.2988i	−0.905586	−	0.522841i
$389$	12.3500	+	21.3909i	0.626171	+	1.08456i	0.988313	+	0.152437i	$0.0487122\pi$
$389$	12.3500	+	21.3909i	0.626171	+	1.08456i	−0.362142	+	0.932123i	$0.617955\pi$
$390$	3.75812	+	3.08607i	0.190300	+	0.156269i
$391$	−10.5853			−0.535320
$392$	19.4692	−	3.43690i	0.983345	−	0.173590i
$393$	3.04778	+	5.27892i	0.153740	+	0.266286i
$394$	9.16847	+	15.8803i	0.461901	+	0.800036i
$395$	15.5008	−	8.94941i	0.779932	−	0.450294i
$396$		−	4.48467i		−	0.225363i
$397$	13.7267	−	7.92513i	0.688925	−	0.397751i	−0.114284	−	0.993448i	$-0.536458\pi$
$397$	13.7267	−	7.92513i	0.688925	−	0.397751i	0.803209	+	0.595697i	$0.203124\pi$
$398$		−	0.948061i		−	0.0475220i
$399$	0.998094	−	1.18972i	0.0499672	−	0.0595605i
$400$	−0.0243695	−	0.0422091i	−0.00121847	−	0.00211046i
$401$			38.0735i			1.90130i	0.310267	+	0.950650i	$0.399582\pi$
$401$			38.0735i			1.90130i	−0.310267	+	0.950650i	$0.600418\pi$
$402$	0.837033	+	1.44978i	0.0417474	+	0.0723086i
$403$	23.7722	−	28.9491i	1.18418	−	1.44205i
$404$	−8.12307	+	14.0696i	−0.404138	+	0.699987i
$405$	−1.34003	+	0.773665i	−0.0665865	+	0.0384437i
$406$	−4.88551	−	0.860952i	−0.242464	−	0.0427284i
$407$	−10.5039	+	18.1932i	−0.520658	+	0.901806i
$408$	−11.3297	−	6.54120i	−0.560903	−	0.323838i
$409$		−	5.91319i		−	0.292389i	−0.989256	−	0.146194i	$-0.953298\pi$
$409$		−	5.91319i		−	0.292389i	0.989256	−	0.146194i	$-0.0467025\pi$
$410$			2.49933i			0.123433i
$411$	−2.13982	−	1.23543i	−0.105550	−	0.0609392i
$412$	−0.104317	+	0.180682i	−0.00513931	+	0.00890154i
$413$	9.20800	−	10.9759i	0.453096	−	0.540087i
$414$	1.72503	−	0.995945i	0.0847805	−	0.0489480i
$415$	7.31268	−	12.6659i	0.358965	−	0.621746i
$416$	7.18915	+	19.1183i	0.352477	+	0.937350i
$417$	−5.27760	−	9.14107i	−0.258445	−	0.447640i
$418$			1.84997i			0.0904850i
$419$	−6.63834	−	11.4979i	−0.324304	−	0.561711i	0.657067	−	0.753832i	$-0.271797\pi$
$419$	−6.63834	−	11.4979i	−0.324304	−	0.561711i	−0.981371	+	0.192121i	$0.938463\pi$
$420$	−5.00033	−	0.881186i	−0.243991	−	0.0429975i
$421$		−	23.3548i		−	1.13824i	−0.822254	−	0.569121i	$-0.807284\pi$
$421$		−	23.3548i		−	1.13824i	0.822254	−	0.569121i	$-0.192716\pi$
$422$	15.4014	−	8.89198i	0.749727	−	0.432855i
$423$		−	2.42663i		−	0.117987i
$424$	31.7655	−	18.3398i	1.54267	−	0.890659i
$425$	−6.03503	−	10.4530i	−0.292742	−	0.507044i
$426$	4.60348	+	7.97346i	0.223039	+	0.386315i
$427$	4.45785	−	25.2963i	0.215730	−	1.22417i
$428$	−1.96284			−0.0948776
$429$	−8.27388	+	10.0757i	−0.399467	+	0.486458i
$430$	−5.31051	−	9.19808i	−0.256096	−	0.443571i
$431$	−6.25962	−	3.61400i	−0.301515	−	0.174080i	0.341608	−	0.939843i	$-0.389028\pi$
$431$	−6.25962	−	3.61400i	−0.301515	−	0.174080i	−0.643123	+	0.765762i	$0.722362\pi$
$432$	−0.0187042			−0.000899907
$433$	−11.8710	+	20.5611i	−0.570482	+	0.988103i	0.426035	+	0.904707i	$0.359910\pi$
$433$	−11.8710	+	20.5611i	−0.570482	+	0.988103i	−0.996516	+	0.0833965i	$0.973423\pi$
$434$	4.15811	−	23.5954i	0.199596	−	1.13261i
$435$	2.88257	+	1.66425i	0.138208	+	0.0797947i
$436$	4.67399	−	2.69853i	0.223843	−	0.129236i
$437$	1.16162	−	0.670664i	0.0555680	−	0.0320822i
$438$	1.98055			0.0946344
$439$	−28.4573			−1.35819			−0.679097	−	0.734048i	$-0.737629\pi$
$439$	−28.4573			−1.35819			−0.679097	+	0.734048i	$0.737629\pi$
$440$	13.6852	−	7.90114i	0.652415	−	0.376672i
$441$	5.36143	−	4.50057i	0.255306	−	0.214313i
$442$	5.12378	+	13.6258i	0.243713	+	0.648112i
$443$	−10.4345	+	18.0731i	−0.495760	+	0.858681i	−0.999988	−	0.00488943i	$-0.998444\pi$
$443$	−10.4345	+	18.0731i	−0.495760	+	0.858681i	0.504228	+	0.863570i	$0.331777\pi$
$444$	6.24016	+	3.60276i	0.296145	+	0.170979i
$445$	−9.80013	+	16.9743i	−0.464571	+	0.804660i
$446$	4.81238	+	8.33528i	0.227873	+	0.394687i
$447$		−	12.0561i		−	0.570233i
$448$	9.93273	+	8.33288i	0.469277	+	0.393692i
$449$	5.13399	+	2.96411i	0.242288	+	0.139885i	0.616228	−	0.787568i	$-0.288660\pi$
$449$	5.13399	+	2.96411i	0.242288	+	0.139885i	−0.373940	+	0.927453i	$0.621993\pi$
$450$	1.96699	+	1.13565i	0.0927250	+	0.0535348i
$451$	−6.70080			−0.315528
$452$	8.21373	−	14.2266i	0.386341	−	0.669163i
$453$		−	6.75057i		−	0.317169i
$454$	−10.5509			−0.495179
$455$	9.60848	+	11.2050i	0.450453	+	0.525298i
$456$	1.65775			0.0776315
$457$		−	23.2685i		−	1.08845i	−0.838938	−	0.544227i	$-0.816823\pi$
$457$		−	23.2685i		−	1.08845i	0.838938	−	0.544227i	$-0.183177\pi$
$458$	6.25138	−	10.8277i	0.292108	−	0.505946i
$459$	−4.63205			−0.216205
$460$	−3.79796	−	2.19275i	−0.177081	−	0.102238i
$461$	−6.80211	−	3.92720i	−0.316806	−	0.182908i	0.333162	−	0.942870i	$-0.391884\pi$
$461$	−6.80211	−	3.92720i	−0.316806	−	0.182908i	−0.649968	+	0.759962i	$0.725218\pi$
$462$	−1.44722	+	8.21234i	−0.0673310	+	0.382073i
$463$			22.0674i			1.02556i	0.858520	+	0.512780i	$0.171384\pi$
$463$			22.0674i			1.02556i	−0.858520	+	0.512780i	$0.828616\pi$
$464$	0.0201176	+	0.0348446i	0.000933935	+	0.00161762i
$465$	−8.03777	+	13.9218i	−0.372743	+	0.645609i
$466$	−15.9272	−	9.19557i	−0.737813	−	0.425977i
$467$	−5.20349	+	9.01270i	−0.240789	+	0.417058i	−0.960939	−	0.276760i	$-0.910739\pi$
$467$	−5.20349	+	9.01270i	−0.240789	+	0.417058i	0.720150	+	0.693818i	$0.244073\pi$
$468$	3.45589	+	2.83788i	0.159748	+	0.131181i
$469$	1.73842	+	4.77480i	0.0802727	+	0.220480i
$470$	2.83435	−	1.63641i	0.130739	−	0.0754820i
$471$	−2.85664			−0.131627
$472$	15.2938			0.703952
$473$	24.6604	−	14.2377i	1.13389	−	0.654650i
$474$	−8.73190	+	5.04136i	−0.401069	+	0.231558i
$475$	1.32456	+	0.764737i	0.0607751	+	0.0350885i
$476$	−11.6445	−	9.76892i	−0.533723	−	0.447758i
$477$	6.49352	−	11.2471i	0.297318	−	0.514970i
$478$	4.04723			0.185116
$479$	25.3070	+	14.6110i	1.15631	+	0.667595i	0.950417	−	0.310980i	$-0.100657\pi$
$479$	25.3070	+	14.6110i	1.15631	+	0.667595i	0.205892	+	0.978575i	$0.433990\pi$
$480$	−4.38277	−	7.59118i	−0.200045	−	0.346489i
$481$	−7.37290	−	19.6069i	−0.336175	−	0.893998i
$482$	−7.00788			−0.319200
$483$	5.68131	−	2.06846i	0.258509	−	0.0941182i
$484$	1.28682	+	2.22883i	0.0584916	+	0.101311i
$485$	−12.8487	−	22.2546i	−0.583430	−	1.01053i
$486$	0.754861	−	0.435819i	0.0342412	−	0.0197692i
$487$			41.0749i			1.86128i	0.365933	+	0.930641i	$0.380750\pi$
$487$			41.0749i			1.86128i	−0.365933	+	0.930641i	$0.619250\pi$
$488$	23.7462	−	13.7099i	1.07494	−	0.620616i
$489$			17.1937i			0.777527i
$490$	8.87226	+	3.22726i	0.400808	+	0.145793i
$491$	−6.32263	−	10.9511i	−0.285336	−	0.494217i	0.687355	−	0.726322i	$-0.258772\pi$
$491$	−6.32263	−	10.9511i	−0.285336	−	0.494217i	−0.972691	+	0.232105i	$0.925439\pi$
$492$			2.29833i			0.103617i
$493$	4.98206	+	8.62918i	0.224381	+	0.388639i
$494$	−1.42559	−	1.17066i	−0.0641402	−	0.0526703i
$495$	2.79753	−	4.84547i	0.125740	−	0.217788i
$496$	−0.168288	+	0.0971611i	−0.00755635	+	0.00436266i
$497$	9.56087	+	26.2603i	0.428864	+	1.17793i
$498$	−4.11936	+	7.13495i	−0.184593	+	0.319725i
$499$	12.8737	+	7.43261i	0.576304	+	0.332729i	0.759663	−	0.650317i	$-0.225364\pi$
$499$	12.8737	+	7.43261i	0.576304	+	0.332729i	−0.183359	+	0.983046i	$0.558697\pi$
$500$		−	14.5960i		−	0.652753i
$501$		−	13.6862i		−	0.611456i
$502$	−9.40079	−	5.42755i	−0.419578	−	0.242243i
$503$	−13.9385	+	24.1422i	−0.621488	+	1.07645i	0.367721	+	0.929936i	$0.380138\pi$
$503$	−13.9385	+	24.1422i	−0.621488	+	1.07645i	−0.989209	+	0.146513i	$0.953195\pi$
$504$	7.35906	+	1.29685i	0.327799	+	0.0577665i
$505$	−17.5532	+	10.1343i	−0.781106	+	0.450972i
$506$	−3.60129	+	6.23762i	−0.160097	+	0.277296i
$507$	−2.52863	−	12.7517i	−0.112300	−	0.566323i
$508$	2.16680	+	3.75301i	0.0961363	+	0.166513i
$509$		−	31.6545i		−	1.40306i	−0.712640	−	0.701530i	$-0.752501\pi$
$509$		−	31.6545i		−	1.40306i	0.712640	−	0.701530i	$-0.247499\pi$
$510$	−3.12365	−	5.41032i	−0.138317	−	0.239573i
$511$	5.92049	+	1.04334i	0.261907	+	0.0461547i
$512$		−	0.211612i		−	0.00935202i
$513$	0.508319	−	0.293478i	0.0224428	−	0.0129574i
$514$		−	6.25187i		−	0.275758i
$515$	−0.225418	+	0.130145i	−0.00993310	+	0.00573488i
$516$	−4.88343	−	8.45836i	−0.214981	−	0.372358i
$517$	4.38728	+	7.59900i	0.192952	+	0.334203i
$518$	−10.2644	−	8.61111i	−0.450991	−	0.378350i
$519$	−18.3145			−0.803918
$520$	−2.57132	+	15.5456i	−0.112760	+	0.681720i
$521$	16.3636	+	28.3425i	0.716901	+	1.24171i	0.962222	+	0.272267i	$0.0877733\pi$
$521$	16.3636	+	28.3425i	0.716901	+	1.24171i	−0.245321	+	0.969442i	$0.578893\pi$
$522$	−1.62380	−	0.937502i	−0.0710718	−	0.0410333i
$523$	−3.04966			−0.133352			−0.0666761	−	0.997775i	$-0.521239\pi$
$523$	−3.04966			−0.133352			−0.0666761	+	0.997775i	$0.521239\pi$
$524$	−3.78000	+	6.54716i	−0.165130	+	0.286014i
$525$	5.28172	+	4.43100i	0.230513	+	0.193385i
$526$	13.1014	+	7.56411i	0.571249	+	0.329811i
$527$	−41.6760	+	24.0617i	−1.81544	+	1.04814i
$528$	0.0585724	−	0.0338168i	0.00254903	−	0.00147169i
$529$	−17.7777			−0.772945
$530$	17.5158			0.760837
$531$	4.68954	−	2.70751i	0.203509	−	0.117496i
$532$	1.89680	+	0.334265i	0.0822368	+	0.0144922i
$533$	4.24024	−	5.16364i	0.183665	−	0.223662i
$534$	5.52059	−	9.56194i	0.238899	−	0.413785i
$535$	−2.12076	−	1.22442i	−0.0916884	−	0.0529363i
$536$	−2.71219	+	4.69766i	−0.117149	+	0.202908i
$537$	−9.18131	−	15.9025i	−0.396203	−	0.686243i
$538$		−	9.77034i		−	0.421229i
$539$	−8.65242	+	23.7869i	−0.372686	+	1.02457i
$540$	−1.66196	−	0.959535i	−0.0715195	−	0.0412918i
$541$	−31.3496	−	18.0997i	−1.34782	−	0.778166i	−0.359883	−	0.932998i	$-0.617183\pi$
$541$	−31.3496	−	18.0997i	−1.34782	−	0.778166i	−0.987941	+	0.154831i	$0.950517\pi$
$542$	−22.3416			−0.959656
$543$	−9.01243	+	15.6100i	−0.386760	+	0.669889i
$544$		−	26.2403i		−	1.12504i
$545$	6.73336			0.288425
$546$	−5.41263	−	6.31197i	−0.231639	−	0.270127i
$547$	−14.4610			−0.618310			−0.309155	−	0.951012i	$-0.600046\pi$
$547$	−14.4610			−0.618310			−0.309155	+	0.951012i	$0.600046\pi$
$548$		−	3.06447i		−	0.130908i
$549$	4.85421	−	8.40774i	0.207173	−	0.358833i
$550$	−8.21287			−0.350198
$551$	−1.09346	−	0.631309i	−0.0465829	−	0.0268947i
$552$	5.58952	+	3.22711i	0.237906	+	0.137355i
$553$	−28.7582	+	10.4703i	−1.22292	+	0.445243i
$554$			10.8137i			0.459429i
$555$	4.49480	+	7.78521i	0.190793	+	0.330464i
$556$	6.54552	−	11.3372i	0.277592	−	0.480803i
$557$	−20.3907	−	11.7726i	−0.863983	−	0.498821i	0.00136123	−	0.999999i	$-0.499567\pi$
$557$	−20.3907	−	11.7726i	−0.863983	−	0.498821i	−0.865344	+	0.501178i	$0.832900\pi$
$558$	4.52782	−	7.84241i	0.191678	−	0.331996i
$559$	−4.63346	+	28.0129i	−0.195974	+	1.18482i
$560$	−0.0261963	−	0.0719518i	−0.00110700	−	0.00304052i
$561$	14.5053	−	8.37462i	0.612413	−	0.353577i
$562$	26.9023			1.13480
$563$	−30.6510			−1.29179			−0.645894	−	0.763427i	$-0.723515\pi$
$563$	−30.6510			−1.29179			−0.645894	+	0.763427i	$0.723515\pi$
$564$	2.60640	−	1.50481i	0.109749	−	0.0633638i
$565$	17.7491	−	10.2474i	0.746709	−	0.431113i
$566$	8.10355	+	4.67859i	0.340618	+	0.196656i
$567$	2.48610	−	0.905145i	0.104407	−	0.0380125i
$568$	−14.9164	+	25.8360i	−0.625878	+	1.08405i
$569$	18.2733			0.766057			0.383028	−	0.923737i	$-0.374881\pi$
$569$	18.2733			0.766057			0.383028	+	0.923737i	$0.374881\pi$
$570$	0.685576	+	0.395818i	0.0287156	+	0.0165790i
$571$	9.31271	+	16.1301i	0.389725	+	0.675023i	0.992412	−	0.122954i	$-0.0392369\pi$
$571$	9.31271	+	16.1301i	0.389725	+	0.675023i	−0.602688	+	0.797977i	$0.705904\pi$
$572$	−15.9530	−	2.63869i	−0.667026	−	0.110329i
$573$	−24.3981			−1.01924
$574$	0.741681	−	4.20870i	0.0309572	−	0.175668i
$575$	2.97739	+	5.15699i	0.124166	+	0.215061i
$576$	2.45019	+	4.24385i	0.102091	+	0.176827i
$577$	−17.9758	+	10.3783i	−0.748341	+	0.432055i	−0.825094	−	0.564995i	$-0.808878\pi$
$577$	−17.9758	+	10.3783i	−0.748341	+	0.432055i	0.0767533	+	0.997050i	$0.475545\pi$
$578$		−	3.88389i		−	0.161549i
$579$	−10.4054	+	6.00758i	−0.432435	+	0.249666i
$580$			4.12816i			0.171413i
$581$	−16.0727	+	19.1586i	−0.666809	+	0.794831i
$582$	7.23792	+	12.5364i	0.300021	+	0.519652i
$583$			46.9605i			1.94490i
$584$	3.20874	+	5.55769i	0.132778	+	0.229979i
$585$	1.96365	+	5.22198i	0.0811869	+	0.215902i
$586$	−0.00689879	+	0.0119491i	−0.000284986	+	0.000493611i
$587$	12.5550	−	7.24864i	0.518201	−	0.299183i	−0.217998	−	0.975949i	$-0.569952\pi$
$587$	12.5550	−	7.24864i	0.518201	−	0.299183i	0.736198	+	0.676766i	$0.236619\pi$
$588$	8.15874	+	2.96772i	0.336461	+	0.122387i
$589$	3.04901	−	5.28104i	0.125632	−	0.217601i
$590$	6.32484	+	3.65165i	0.260389	+	0.150336i
$591$			21.0373i			0.865360i
$592$			0.108667i			0.00446618i
$593$	4.53361	+	2.61748i	0.186173	+	0.107487i	0.590190	−	0.807265i	$-0.299053\pi$
$593$	4.53361	+	2.61748i	0.186173	+	0.107487i	−0.404017	+	0.914752i	$0.632386\pi$
$594$	−1.57590	+	2.72954i	−0.0646600	+	0.111994i
$595$	−6.48745	−	17.8187i	−0.265959	−	0.730494i
$596$	12.9493	−	7.47626i	0.530422	−	0.306239i
$597$	0.543838	−	0.941956i	0.0222578	−	0.0385517i
$598$	−2.52782	−	6.72230i	−0.103370	−	0.274895i
$599$	−7.47791	−	12.9521i	−0.305539	−	0.529209i	0.671842	−	0.740694i	$-0.265503\pi$
$599$	−7.47791	−	12.9521i	−0.305539	−	0.529209i	−0.977381	+	0.211485i	$0.932170\pi$
$600$			7.35954i			0.300452i
$601$	−23.0757	−	39.9683i	−0.941278	−	1.63034i	−0.763038	−	0.646354i	$-0.776293\pi$
$601$	−23.0757	−	39.9683i	−0.941278	−	1.63034i	−0.178240	−	0.983987i	$-0.557040\pi$
$602$	6.21301	+	17.0649i	0.253223	+	0.695512i
$603$			1.92060i			0.0782127i
$604$	7.25068	−	4.18618i	0.295026	−	0.170333i
$605$			3.21086i			0.130540i
$606$	9.88801	−	5.70885i	0.401673	−	0.231906i
$607$	21.8090	+	37.7743i	0.885201	+	1.53321i	0.845484	+	0.534001i	$0.179312\pi$
$607$	21.8090	+	37.7743i	0.885201	+	1.53321i	0.0397170	+	0.999211i	$0.487354\pi$
$608$	1.66254	+	2.87960i	0.0674249	+	0.116783i
$609$	−4.36018	−	3.65790i	−0.176684	−	0.148225i
$610$	13.0939			0.530155
$611$	−8.63205	−	1.42778i	−0.349215	−	0.0577618i
$612$	−2.87244	−	4.97521i	−0.116111	−	0.201111i
$613$	15.6112	+	9.01312i	0.630530	+	0.364036i	0.780957	−	0.624585i	$-0.214732\pi$
$613$	15.6112	+	9.01312i	0.630530	+	0.364036i	−0.150428	+	0.988621i	$0.548065\pi$
$614$	−19.8718			−0.801960
$615$	−1.43370	+	2.48323i	−0.0578122	+	0.100134i
$616$	−25.3896	+	9.24389i	−1.02298	+	0.372447i
$617$	32.3120	+	18.6554i	1.30083	+	0.751036i	0.980547	−	0.196285i	$-0.0628876\pi$
$617$	32.3120	+	18.6554i	1.30083	+	0.751036i	0.320286	+	0.947321i	$0.396221\pi$
$618$	0.126982	−	0.0733131i	0.00510796	−	0.00294908i
$619$	−0.272738	+	0.157465i	−0.0109623	+	0.00632906i	−0.505471	−	0.862844i	$-0.668681\pi$
$619$	−0.272738	+	0.157465i	−0.0109623	+	0.00632906i	0.494509	+	0.869173i	$0.335348\pi$
$620$	−19.9376			−0.800715
$621$	2.28523			0.0917030
$622$	2.71133	−	1.56539i	0.108715	−	0.0627664i
$623$	21.5399	−	25.6754i	0.862979	−	1.02866i
$624$	−0.0110052	+	0.0665350i	−0.000440560	+	0.00266353i
$625$	2.59055	−	4.48697i	0.103622	−	0.179479i
$626$	−6.16569	−	3.55976i	−0.246431	−	0.142277i
$627$	−1.06120	+	1.83806i	−0.0423804	+	0.0734049i
$628$	−1.77147	−	3.06827i	−0.0706893	−	0.122437i
$629$			26.9110i			1.07301i
$630$	2.73375	+	2.29343i	0.108915	+	0.0913723i
$631$	22.1441	+	12.7849i	0.881542	+	0.508958i	0.871166	−	0.490988i	$-0.163364\pi$
$631$	22.1441	+	12.7849i	0.881542	+	0.508958i	0.0103751	+	0.999946i	$0.496697\pi$
$632$	−28.2935	−	16.3353i	−1.12546	−	0.649782i
$633$	20.4029			0.810943
$634$	9.87217	−	17.0991i	0.392074	−	0.679092i
$635$			5.40660i			0.214554i
$636$	16.1071			0.638689
$637$	−12.8550	−	21.7198i	−0.509332	−	0.860570i
$638$	6.77992			0.268420
$639$			10.5628i			0.417858i
$640$	5.46094	−	9.45863i	0.215863	−	0.373885i
$641$	15.3433			0.606026			0.303013	−	0.952986i	$-0.402007\pi$
$641$	15.3433			0.606026			0.303013	+	0.952986i	$0.402007\pi$
$642$	1.19466	+	0.689738i	0.0471495	+	0.0272218i
$643$	−13.2667	−	7.65954i	−0.523188	−	0.302063i	0.215050	−	0.976603i	$-0.431009\pi$
$643$	−13.2667	−	7.65954i	−0.523188	−	0.302063i	−0.738238	+	0.674540i	$0.764342\pi$
$644$	5.74481	+	4.81951i	0.226377	+	0.189915i
$645$		−	12.1851i		−	0.479789i
$646$	1.18491	+	2.05232i	0.0466196	+	0.0807476i
$647$	−9.23247	+	15.9911i	−0.362966	+	0.628675i	−0.988448	−	0.151563i	$-0.951569\pi$
$647$	−9.23247	+	15.9911i	−0.362966	+	0.628675i	0.625482	+	0.780239i	$0.284903\pi$
$648$	2.44594	+	1.41216i	0.0960854	+	0.0554749i
$649$	−9.79021	+	16.9571i	−0.384299	+	0.665626i
$650$	5.19708	−	6.32884i	0.203846	−	0.248238i
$651$	17.6664	−	21.0582i	0.692401	−	0.825337i
$652$	−18.4675	+	10.6622i	−0.723244	+	0.417565i
$653$	32.2841			1.26337			0.631687	−	0.775223i	$-0.282363\pi$
$653$	32.2841			1.26337			0.631687	+	0.775223i	$0.282363\pi$
$654$	−3.79302			−0.148319
$655$	−8.16822	+	4.71593i	−0.319159	+	0.184266i
$656$	−0.0300175	+	0.0173306i	−0.00117199	+	0.000676646i
$657$	1.96780	+	1.13611i	0.0767710	+	0.0443238i
$658$	−5.25846	+	1.91451i	−0.204996	+	0.0746353i
$659$	−1.93680	+	3.35464i	−0.0754471	+	0.130678i	−0.901281	−	0.433236i	$-0.857372\pi$
$659$	−1.93680	+	3.35464i	−0.0754471	+	0.130678i	0.825834	+	0.563914i	$0.190705\pi$
$660$	6.93926			0.270110
$661$	21.7811	+	12.5753i	0.847185	+	0.489123i	0.859700	−	0.510799i	$-0.170650\pi$
$661$	21.7811	+	12.5753i	0.847185	+	0.489123i	−0.0125149	+	0.999922i	$0.503984\pi$
$662$	7.82373	+	13.5511i	0.304078	+	0.526679i
$663$	−2.72540	+	16.4772i	−0.105846	+	0.639922i
$664$	−26.6955			−1.03599
$665$	1.84089	+	1.54438i	0.0713866	+	0.0598885i
$666$	−2.53200	−	4.38555i	−0.0981130	−	0.169937i
$667$	−2.45790	−	4.25722i	−0.0951704	−	0.164840i
$668$	14.7002	−	8.48716i	0.568768	−	0.328378i
$669$			11.0421i			0.426914i
$670$	−2.24329	+	1.29517i	−0.0866660	+	0.0500366i
$671$			35.1052i			1.35522i
$672$	5.12760	+	14.0837i	0.197801	+	0.543289i
$673$	5.11747	+	8.86372i	0.197264	+	0.341671i	0.947640	−	0.319339i	$-0.103461\pi$
$673$	5.11747	+	8.86372i	0.197264	+	0.341671i	−0.750376	+	0.661011i	$0.770128\pi$
$674$			4.56080i			0.175675i
$675$	1.30289	+	2.25666i	0.0501481	+	0.0868590i
$676$	12.1284	−	10.6236i	0.466475	−	0.408600i
$677$	−14.7224	+	25.4999i	−0.565827	+	0.980041i	0.431146	+	0.902282i	$0.358110\pi$
$677$	−14.7224	+	25.4999i	−0.565827	+	0.980041i	−0.996972	+	0.0777582i	$0.975224\pi$
$678$	−9.99837	+	5.77256i	−0.383985	+	0.221694i
$679$	15.0323	+	41.2882i	0.576886	+	1.58450i
$680$	10.1214	−	17.5308i	0.388138	−	0.672274i
$681$	−10.4830	−	6.05235i	−0.401709	−	0.231927i
$682$			32.7447i			1.25386i
$683$		−	18.8866i		−	0.722675i	−0.932435	−	0.361338i	$-0.882320\pi$
$683$		−	18.8866i		−	0.722675i	0.932435	−	0.361338i	$-0.117680\pi$
$684$	0.630441	+	0.363985i	0.0241055	+	0.0139173i
$685$	1.91161	−	3.31101i	0.0730390	−	0.126507i
$686$	−13.9826	−	8.06736i	−0.533858	−	0.308013i
$687$	12.4222	−	7.17199i	0.473938	−	0.273628i
$688$	0.0736473	−	0.127561i	0.00280778	−	0.00486321i
$689$	−36.1878	−	29.7164i	−1.37864	−	1.13211i
$690$	1.54106	+	2.66919i	0.0586670	+	0.101614i
$691$			4.84472i			0.184302i	0.995745	+	0.0921508i	$0.0293742\pi$
$691$			4.84472i			0.184302i	−0.995745	+	0.0921508i	$0.970626\pi$
$692$	−11.3573	−	19.6714i	−0.431738	−	0.747793i
$693$	−6.14877	+	7.32928i	−0.233572	+	0.278416i
$694$		−	14.2241i		−	0.539939i
$695$	14.1442	−	8.16618i	0.536522	−	0.309761i
$696$		−	6.07548i		−	0.230290i
$697$	−7.43374	+	4.29187i	−0.281573	+	0.162566i
$698$	−11.8934	−	20.6000i	−0.450172	−	0.779721i
$699$	−10.5498	−	18.2727i	−0.399028	−	0.691137i
$700$	−1.48396	+	8.42078i	−0.0560883	+	0.318276i
$701$	3.10557			0.117296			0.0586479	−	0.998279i	$-0.481321\pi$
$701$	3.10557			0.117296			0.0586479	+	0.998279i	$0.481321\pi$
$702$	−1.10616	−	2.94163i	−0.0417493	−	0.111025i
$703$	−1.70503	−	2.95320i	−0.0643066	−	0.111382i
$704$	−15.3456	−	8.85976i	−0.578358	−	0.333915i
$705$	3.75479			0.141414
$706$	12.3821	−	21.4465i	0.466008	−	0.807149i
$707$	32.5658	−	11.8566i	1.22476	−	0.445913i
$708$	5.81618	+	3.35798i	0.218586	+	0.126200i
$709$	14.3519	−	8.28608i	0.538997	−	0.311190i	−0.205675	−	0.978620i	$-0.565939\pi$
$709$	14.3519	−	8.28608i	0.538997	−	0.311190i	0.744672	+	0.667430i	$0.232606\pi$
$710$	−12.3376	+	7.12310i	−0.463021	+	0.267325i
$711$	−11.5676			−0.433817
$712$	35.7761			1.34077
$713$	20.5609	−	11.8709i	0.770012	−	0.444567i
$714$	3.65449	+	10.0376i	0.136766	+	0.375647i
$715$	−15.5904	−	12.8024i	−0.583047	−	0.478783i
$716$	11.3871	−	19.7230i	0.425555	−	0.737084i
$717$	4.02116	+	2.32162i	0.150173	+	0.0867025i
$718$	2.41224	−	4.17813i	0.0900241	−	0.155926i
$719$	−8.40488	−	14.5577i	−0.313449	−	0.542910i	0.665658	−	0.746257i	$-0.268151\pi$
$719$	−8.40488	−	14.5577i	−0.313449	−	0.542910i	−0.979107	+	0.203348i	$0.934818\pi$
$720$		−	0.0289416i		−	0.00107859i
$721$	0.418210	−	0.152263i	0.0155750	−	0.00567055i
$722$	14.0823	+	8.13042i	0.524089	+	0.302583i
$723$	−6.96275	−	4.01995i	−0.258948	−	0.149503i
$724$	−22.3553			−0.830827
$725$	2.80267	−	4.85437i	0.104089	−	0.180287i
$726$		−	1.80873i		−	0.0671284i
$727$	36.2622			1.34489			0.672444	−	0.740148i	$-0.265244\pi$
$727$	36.2622			1.34489			0.672444	+	0.740148i	$0.265244\pi$
$728$	8.94312	−	25.4148i	0.331454	−	0.941933i
$729$	1.00000			0.0370370
$730$			3.06456i			0.113425i
$731$	18.2385	−	31.5901i	0.674577	−	1.16840i
$732$	12.0408			0.445042
$733$	−1.19882	−	0.692138i	−0.0442794	−	0.0255647i	0.477697	−	0.878525i	$-0.341472\pi$
$733$	−1.19882	−	0.692138i	−0.0442794	−	0.0255647i	−0.521976	+	0.852960i	$0.674805\pi$
$734$	−20.0607	−	11.5820i	−0.740454	−	0.427501i
$735$	6.96386	+	8.29589i	0.256866	+	0.305999i
$736$			12.9457i			0.477184i
$737$	−3.47239	−	6.01436i	−0.127907	−	0.221542i
$738$	0.807626	−	1.39885i	0.0297291	−	0.0514924i
$739$	36.5792	+	21.1190i	1.34559	+	0.776876i	0.987621	−	0.156859i	$-0.0501367\pi$
$739$	36.5792	+	21.1190i	1.34559	+	0.776876i	0.357967	+	0.933734i	$0.383470\pi$
$740$	−5.57465	+	9.65558i	−0.204928	+	0.354946i
$741$	−0.744881	−	1.98088i	−0.0273639	−	0.0727694i
$742$	−29.4954	−	5.19785i	−1.08281	−	0.190819i
$743$	−10.7785	+	6.22298i	−0.395425	+	0.228299i	−0.684508	−	0.729005i	$-0.739983\pi$
$743$	−10.7785	+	6.22298i	−0.395425	+	0.228299i	0.289083	+	0.957304i	$0.406650\pi$
$744$	29.3425			1.07575
$745$	18.6547			0.683457
$746$	12.1660	−	7.02407i	0.445430	−	0.257169i
$747$	−8.18567	+	4.72600i	−0.299498	+	0.172915i
$748$	17.9901	+	10.3866i	0.657784	+	0.379772i
$749$	3.20787	+	2.69118i	0.117213	+	0.0983337i
$750$	−5.12900	+	8.88368i	−0.187284	+	0.324386i
$751$	−30.0111			−1.09512			−0.547560	−	0.836766i	$-0.684443\pi$
$751$	−30.0111			−1.09512			−0.547560	+	0.836766i	$0.684443\pi$
$752$	0.0393073	+	0.0226941i	0.00143339	+	0.000827568i
$753$	−6.22683	−	10.7852i	−0.226918	−	0.393034i
$754$	−4.29031	+	5.22461i	−0.156244	+	0.190269i
$755$	10.4454			0.380145
$756$	2.51389	+	2.10899i	0.0914294	+	0.0767031i
$757$	−19.8603	−	34.3991i	−0.721835	−	1.25026i	−0.960263	−	0.279095i	$-0.909965\pi$
$757$	−19.8603	−	34.3991i	−0.721835	−	1.25026i	0.238428	−	0.971160i	$-0.423368\pi$
$758$	−3.74068	−	6.47906i	−0.135868	−	0.235330i
$759$	−7.15620	+	4.13163i	−0.259753	+	0.149969i
$760$			2.56509i			0.0930457i
$761$	6.49915	−	3.75229i	0.235594	−	0.136020i	−0.377556	−	0.925987i	$-0.623235\pi$
$761$	6.49915	−	3.75229i	0.235594	−	0.136020i	0.613150	+	0.789966i	$0.289902\pi$
$762$		−	3.04563i		−	0.110332i
$763$	−11.3385	−	1.99814i	−0.410483	−	0.0723375i
$764$	−15.1298	−	26.2056i	−0.547377	−	0.948085i
$765$		−	7.16730i		−	0.259134i
$766$	−0.393850	−	0.682169i	−0.0142304	−	0.0246478i
$767$	−6.87196	−	18.2748i	−0.248132	−	0.659863i
$768$	−7.97663	+	13.8159i	−0.287832	+	0.498539i
$769$	13.1246	−	7.57747i	0.473284	−	0.273251i	−0.244329	−	0.969692i	$-0.578568\pi$
$769$	13.1246	−	7.57747i	0.473284	−	0.273251i	0.717613	+	0.696442i	$0.245234\pi$
$770$	−12.7072	−	2.23933i	−0.457936	−	0.0806999i
$771$	3.58628	−	6.21162i	0.129157	−	0.223706i
$772$	−12.9053	−	7.45088i	−0.464472	−	0.268163i
$773$			10.4241i			0.374929i	0.982271	+	0.187464i	$0.0600269\pi$
$773$			10.4241i			0.374929i	−0.982271	+	0.187464i	$0.939973\pi$
$774$			6.86410i			0.246725i
$775$	23.4450	+	13.5360i	0.842168	+	0.486226i
$776$	−23.4526	+	40.6211i	−0.841900	+	1.45821i
$777$	−5.25866	−	14.4436i	−0.188653	−	0.518162i
$778$	18.6451	−	10.7648i	0.668459	−	0.385935i
$779$	0.543851	−	0.941977i	0.0194855	−	0.0337498i
$780$	−4.39114	+	5.34740i	−0.157228	+	0.191468i
$781$	−19.0973	−	33.0775i	−0.683355	−	1.18361i
$782$			9.22653i			0.329940i
$783$	−1.07556	−	1.86293i	−0.0384375	−	0.0665757i
$784$	0.0227610	+	0.128936i	0.000812894	+	0.00460485i
$785$		−	4.42016i		−	0.157762i
$786$	4.60131	−	2.65657i	0.164123	−	0.0947566i
$787$		−	13.9207i		−	0.496220i	−0.968732	−	0.248110i	$-0.920190\pi$
$787$		−	13.9207i		−	0.496220i	0.968732	−	0.248110i	$-0.0798095\pi$
$788$	−22.5959	+	13.0457i	−0.804945	+	0.464735i
$789$	8.67804	+	15.0308i	0.308946	+	0.535111i
$790$	−7.80065	−	13.5111i	−0.277535	−	0.480704i
$791$	−32.9292	+	11.9889i	−1.17083	+	0.426277i
$792$	−10.2126			−0.362889
$793$	−27.0520	−	22.2144i	−0.960646	−	0.788858i
$794$	−6.90785	−	11.9647i	−0.245150	−	0.424613i
$795$	17.4030	+	10.0476i	0.617220	+	0.356352i
$796$	1.34899			0.0478136
$797$	21.6516	−	37.5016i	0.766938	−	1.32838i	−0.172278	−	0.985048i	$-0.555113\pi$
$797$	21.6516	−	37.5016i	0.766938	−	1.32838i	0.939216	−	0.343327i	$-0.111554\pi$
$798$	−1.03701	−	0.869977i	−0.0367096	−	0.0307969i
$799$	9.73434	+	5.62012i	0.344376	+	0.198826i
$800$	−12.7839	+	7.38078i	−0.451979	+	0.260950i
$801$	10.9701	−	6.33357i	0.387608	−	0.223786i
$802$	33.1863			1.17185
$803$	−8.21622			−0.289944
$804$	−2.06288	+	1.19101i	−0.0727523	+	0.0420036i
$805$	3.20059	+	8.79086i	0.112806	+	0.309837i
$806$	−25.2331	−	20.7208i	−0.888798	−	0.729858i
$807$	5.60458	−	9.70742i	0.197291	−	0.341717i
$808$	32.0396	+	18.4981i	1.12715	+	0.650760i
$809$	−3.46635	+	6.00389i	−0.121870	+	0.211086i	−0.920505	−	0.390730i	$-0.872223\pi$
$809$	−3.46635	+	6.00389i	−0.121870	+	0.211086i	0.798635	+	0.601816i	$0.205556\pi$
$810$	0.674356	+	1.16802i	0.0236945	+	0.0410400i
$811$		−	9.46114i		−	0.332226i	−0.986107	−	0.166113i	$-0.946878\pi$
$811$		−	9.46114i		−	0.332226i	0.986107	−	0.166113i	$-0.0531216\pi$
$812$	1.22504	−	6.95155i	0.0429905	−	0.243952i
$813$	−22.1978	−	12.8159i	−0.778510	−	0.449473i
$814$	15.8579	+	9.15558i	0.555820	+	0.320903i
$815$	−26.6044			−0.931910
$816$	0.0433194	−	0.0750314i	0.00151648	−	0.00262662i
$817$			4.62225i			0.161712i
$818$	−5.15417			−0.180211
$819$	−1.75702	−	9.37619i	−0.0613954	−	0.327630i
$820$	−3.55627			−0.124190
$821$		−	21.0073i		−	0.733158i	−0.930387	−	0.366579i	$-0.880529\pi$
$821$		−	21.0073i		−	0.733158i	0.930387	−	0.366579i	$-0.119471\pi$
$822$	−1.07685	+	1.86515i	−0.0375593	+	0.0650547i
$823$	−32.7312			−1.14094			−0.570469	−	0.821319i	$-0.693239\pi$
$823$	−32.7312			−1.14094			−0.570469	+	0.821319i	$0.693239\pi$
$824$	0.411453	+	0.237552i	0.0143336	+	0.00827553i
$825$	−8.15998	−	4.71117i	−0.284094	−	0.164022i
$826$	−9.56698	−	8.02604i	−0.332878	−	0.279262i
$827$			5.50483i			0.191422i	0.995409	+	0.0957109i	$0.0305124\pi$
$827$			5.50483i			0.191422i	−0.995409	+	0.0957109i	$0.969488\pi$
$828$	1.41712	+	2.45453i	0.0492484	+	0.0853007i
$829$	−10.1624	+	17.6019i	−0.352956	+	0.611338i	−0.986766	−	0.162151i	$-0.948157\pi$
$829$	−10.1624	+	17.6019i	−0.352956	+	0.611338i	0.633810	+	0.773489i	$0.281490\pi$
$830$	−11.0401	−	6.37401i	−0.383208	−	0.221245i
$831$	−6.20307	+	10.7440i	−0.215182	+	0.372706i
$832$	16.5380	−	6.21886i	0.573351	−	0.215600i
$833$	5.63671	+	31.9306i	0.195300	+	1.10633i
$834$	−7.96771	+	4.60016i	−0.275899	+	0.159290i
$835$	21.1771			0.732865
$836$	−2.63231			−0.0910402
$837$	8.99732	−	5.19461i	0.310993	−	0.179552i
$838$	−10.0220	+	5.78623i	−0.346206	+	0.199882i
$839$	−48.2439	−	27.8536i	−1.66556	−	0.961614i	−0.969985	−	0.243166i	$-0.921814\pi$
$839$	−48.2439	−	27.8536i	−1.66556	−	0.961614i	−0.695580	−	0.718448i	$-0.744853\pi$
$840$	−2.00666	+	11.3869i	−0.0692364	+	0.392885i
$841$	12.1863	−	21.1073i	0.420218	−	0.727839i
$842$	−20.3569			−0.701546
$843$	26.7290	+	15.4320i	0.920597	+	0.531507i
$844$	12.6523	+	21.9145i	0.435511	+	0.754327i
$845$	19.7311	−	3.91263i	0.678770	−	0.134598i
$846$	−2.11514			−0.0727201
$847$	0.952830	−	5.40688i	0.0327396	−	0.185783i
$848$	0.121456	+	0.210368i	0.00417082	+	0.00722408i
$849$	5.36758	+	9.29692i	0.184215	+	0.319069i
$850$	−9.11121	+	5.26036i	−0.312512	+	0.180429i
$851$		−	13.2766i		−	0.455115i
$852$	−11.3454	+	6.55025i	−0.388686	+	0.224408i
$853$			32.5630i			1.11493i	0.830199	+	0.557467i	$0.188227\pi$
$853$			32.5630i			1.11493i	−0.830199	+	0.557467i	$0.811773\pi$
$854$	−22.0492	−	3.88563i	−0.754508	−	0.132964i
$855$	0.454108	+	0.786537i	0.0155302	+	0.0268990i
$856$			4.46984i			0.152776i
$857$	−3.97771	−	6.88960i	−0.135876	−	0.235344i	0.790056	−	0.613035i	$-0.210052\pi$
$857$	−3.97771	−	6.88960i	−0.135876	−	0.235344i	−0.925932	+	0.377691i	$0.876718\pi$
$858$	8.78234	+	7.21183i	0.299824	+	0.246208i
$859$	15.3344	−	26.5599i	0.523201	−	0.906211i	−0.476434	−	0.879210i	$-0.658071\pi$
$859$	15.3344	−	26.5599i	0.523201	−	0.906211i	0.999635	−	0.0270012i	$-0.00859580\pi$
$860$	13.0879	−	7.55628i	0.446293	−	0.257667i
$861$	3.15115	−	3.75615i	0.107391	−	0.128009i
$862$	−3.15010	+	5.45613i	−0.107293	+	0.185836i
$863$	−20.2659	−	11.7005i	−0.689860	−	0.398291i	0.113699	−	0.993515i	$-0.463730\pi$
$863$	−20.2659	−	11.7005i	−0.689860	−	0.398291i	−0.803560	+	0.595224i	$0.797063\pi$
$864$			5.66495i			0.192726i
$865$		−	28.3386i		−	0.963542i
$866$	17.9218	+	10.3472i	0.609009	+	0.351612i
$867$	2.22793	−	3.85888i	0.0756643	−	0.131054i
$868$	33.5737	+	5.91654i	1.13956	+	0.200820i
$869$	36.2239	−	20.9139i	1.22881	−	0.709454i
$870$	1.45062	−	2.51256i	0.0491808	−	0.0851836i
$871$	6.83198	+	1.13004i	0.231493	+	0.0382900i
$872$	−6.14516	−	10.6437i	−0.208101	−	0.360442i
$873$			16.6076i			0.562082i
$874$	−0.584577	−	1.01252i	−0.0197736	−	0.0342489i
$875$	−20.0121	+	23.8542i	−0.676531	+	0.806419i
$876$			2.81811i			0.0952150i
$877$	10.7865	−	6.22761i	0.364236	−	0.210291i	−0.306702	−	0.951806i	$-0.599225\pi$
$877$	10.7865	−	6.22761i	0.364236	−	0.210291i	0.670937	+	0.741514i	$0.265892\pi$
$878$			24.8045i			0.837111i
$879$	−0.0137087	+	0.00791474i	−0.000462384	+	0.000266957i
$880$	0.0523257	+	0.0906307i	0.00176390	+	0.00305516i
$881$	0.980893	+	1.69896i	0.0330471	+	0.0572393i	0.882076	−	0.471107i	$-0.156146\pi$
$881$	0.980893	+	1.69896i	0.0330471	+	0.0572393i	−0.849029	+	0.528347i	$0.822812\pi$
$882$	−3.92287	−	4.67322i	−0.132090	−	0.157356i
$883$	−32.7262			−1.10132			−0.550662	−	0.834728i	$-0.685625\pi$
$883$	−32.7262			−1.10132			−0.550662	+	0.834728i	$0.685625\pi$
$884$	−19.3880	+	7.29058i	−0.652089	+	0.245209i
$885$	4.18941	+	7.25626i	0.140825	+	0.243917i
$886$	15.7532	+	9.09514i	0.529241	+	0.305557i
$887$	28.7197			0.964313			0.482157	−	0.876085i	$-0.339854\pi$
$887$	28.7197			0.964313			0.482157	+	0.876085i	$0.339854\pi$
$888$	8.20430	−	14.2103i	0.275318	−	0.476865i
$889$	1.60442	−	9.10436i	0.0538106	−	0.305350i
$890$	14.7955	+	8.54217i	0.495945	+	0.286334i
$891$	−3.13150	+	1.80798i	−0.104909	+	0.0605694i
$892$	−11.8602	+	6.84749i	−0.397109	+	0.229271i
$893$	−1.42432			−0.0476632
$894$	−10.5085			−0.351458
$895$	24.6064	−	14.2065i	0.822501	−	0.474871i
$896$	−12.0027	+	14.3072i	−0.400984	+	0.477969i
$897$	1.34458	−	8.12905i	0.0448943	−	0.271421i
$898$	2.58363	−	4.47498i	0.0862170	−	0.149332i
$899$	−19.3544	−	11.1743i	−0.645505	−	0.372682i
$900$	−1.61590	+	2.79882i	−0.0538633	+	0.0932940i
$901$	30.0783	+	52.0971i	1.00205	+	1.73561i
$902$			5.84067i			0.194473i
$903$	−3.61597	+	20.5190i	−0.120332	+	0.682828i
$904$	−32.3972	−	18.7045i	−1.07751	−	0.622103i
$905$	−24.1538	−	13.9452i	−0.802899	−	0.463554i
$906$	−5.88405			−0.195485
$907$	−13.8335	+	23.9603i	−0.459333	+	0.795588i	−0.998926	−	0.0463383i	$-0.985245\pi$
$907$	−13.8335	+	23.9603i	−0.459333	+	0.795588i	0.539593	+	0.841926i	$0.318578\pi$
$908$		−	15.0128i		−	0.498218i
$909$	13.0991			0.434470
$910$	9.76670	−	8.37512i	0.323763	−	0.277633i
$911$	−34.4320			−1.14078			−0.570392	−	0.821373i	$-0.693209\pi$
$911$	−34.4320			−1.14078			−0.570392	+	0.821373i	$0.693209\pi$
$912$			0.0109786i			0.000363536i
$913$	17.0890	−	29.5990i	0.565563	−	0.979584i
$914$	−20.2817			−0.670859
$915$	13.0095	+	7.51106i	0.430082	+	0.248308i
$916$	15.4066	+	8.89503i	0.509050	+	0.293900i
$917$	15.1542	−	5.51737i	0.500436	−	0.182200i
$918$			4.03747i			0.133256i
$919$	−15.7158	−	27.2206i	−0.518417	−	0.897924i	−0.999771	−	0.0213979i	$-0.993188\pi$
$919$	−15.7158	−	27.2206i	−0.518417	−	0.897924i	0.481354	−	0.876526i	$-0.340145\pi$
$920$	−4.99340	+	8.64882i	−0.164628	+	0.285143i
$921$	−19.7438	−	11.3991i	−0.650581	−	0.375613i
$922$	−3.42310	+	5.92898i	−0.112734	+	0.195261i
$923$	37.5742	+	6.21495i	1.23677	+	0.204568i
$924$	−11.6853	−	2.05924i	−0.384417	−	0.0677441i
$925$	13.1106	−	7.56943i	0.431075	−	0.248881i
$926$	19.2348			0.632095
$927$	0.168219			0.00552504
$928$	10.5534	−	6.09301i	0.346432	−	0.200013i
$929$	40.3910	−	23.3198i	1.32519	−	0.765097i	0.340636	−	0.940195i	$-0.389358\pi$
$929$	40.3910	−	23.3198i	1.32519	−	0.765097i	0.984551	+	0.175099i	$0.0560244\pi$
$930$	12.1348	+	7.00603i	0.397916	+	0.229737i
$931$	−2.64164	−	3.14692i	−0.0865762	−	0.103136i
$932$	13.0843	−	22.6627i	0.428590	−	0.742340i
$933$	3.59183			0.117591
$934$	7.85582	+	4.53556i	0.257050	+	0.148408i
$935$	12.9583	+	22.4444i	0.423782	+	0.734012i
$936$	6.46251	−	7.86984i	0.211234	−	0.257234i
$937$	3.16478			0.103389			0.0516945	−	0.998663i	$-0.483538\pi$
$937$	3.16478			0.103389			0.0516945	+	0.998663i	$0.483538\pi$
$938$	4.16190	−	1.51527i	0.135891	−	0.0494754i
$939$	−4.08399	−	7.07368i	−0.133276	−	0.230841i
$940$	2.32843	+	4.03297i	0.0759451	+	0.131541i
$941$	−15.6164	+	9.01615i	−0.509081	+	0.293918i	−0.732456	−	0.680814i	$-0.761626\pi$
$941$	−15.6164	+	9.01615i	−0.509081	+	0.293918i	0.223375	+	0.974733i	$0.428293\pi$
$942$			2.48996i			0.0811272i
$943$	3.66745	−	2.11740i	0.119428	−	0.0689521i
$944$			0.101284i			0.00329650i
$945$	1.40056	+	3.84682i	0.0455601	+	0.125137i
$946$	−12.4101	−	21.4950i	−0.403488	−	0.698862i
$947$			44.6351i			1.45045i	0.688513	+	0.725224i	$0.258264\pi$
$947$			44.6351i			1.45045i	−0.688513	+	0.725224i	$0.741736\pi$
$948$	−7.17331	−	12.4245i	−0.232978	−	0.403530i
$949$	5.19920	−	6.33142i	0.168773	−	0.205527i
$950$	0.666574	−	1.15454i	0.0216265	−	0.0374582i
$951$	19.6172	−	11.3260i	0.636131	−	0.367271i
$952$	−22.2460	+	26.5171i	−0.720999	+	0.859424i
$953$	19.2233	−	33.2957i	0.622702	−	1.07855i	−0.366278	−	0.930505i	$-0.619368\pi$
$953$	19.2233	−	33.2957i	0.622702	−	1.07855i	0.988980	−	0.148047i	$-0.0472986\pi$
$954$	−9.80341	−	5.66000i	−0.317397	−	0.183249i
$955$		−	37.7518i		−	1.22162i
$956$			5.75876i			0.186252i
$957$	6.73626	+	3.88918i	0.217752	+	0.125719i
$958$	12.7355	−	22.0586i	0.411466	−	0.712681i
$959$	−4.20158	+	5.00825i	−0.135676	+	0.161725i
$960$	−6.56664	+	3.79125i	−0.211937	+	0.122362i
$961$	38.4679	−	66.6284i	1.24090	−	2.14930i
$962$	−17.0901	+	6.42650i	−0.551008	+	0.207199i
$963$	0.791312	+	1.37059i	0.0254997	+	0.0441667i
$964$		−	9.97145i		−	0.321159i
$965$	−9.29571	−	16.1006i	−0.299239	−	0.518298i
$966$	−1.80295	−	4.95205i	−0.0580089	−	0.159330i
$967$		−	34.6858i		−	1.11542i	−0.830036	−	0.557710i	$-0.811680\pi$
$967$		−	34.6858i		−	1.11542i	0.830036	−	0.557710i	$-0.188320\pi$
$968$	5.07556	−	2.93037i	0.163135	−	0.0941858i
$969$			2.71881i			0.0873407i
$970$	−19.3980	+	11.1994i	−0.622832	+	0.359592i
$971$	1.89234	+	3.27762i	0.0607280	+	0.105184i	0.894791	−	0.446485i	$-0.147324\pi$
$971$	1.89234	+	3.27762i	0.0607280	+	0.105184i	−0.834063	+	0.551669i	$0.813991\pi$
$972$	0.620123	+	1.07408i	0.0198905	+	0.0344513i
$973$	−26.2413	+	9.55398i	−0.841258	+	0.306287i
$974$	35.8025			1.14719
$975$	8.79404	−	3.30687i	0.281635	−	0.105905i
$976$	0.0907942	+	0.157260i	0.00290625	+	0.00503377i
$977$	−0.219135	−	0.126518i	−0.00701076	−	0.00404767i	0.496491	−	0.868042i	$-0.334622\pi$
$977$	−0.219135	−	0.126518i	−0.00701076	−	0.00404767i	−0.503501	+	0.863994i	$0.667955\pi$
$978$	14.9867			0.479222
$979$	−22.9019	+	39.6672i	−0.731948	+	1.26777i
$980$	−4.59204	+	12.6243i	−0.146687	+	0.403267i
$981$	−3.76860	−	2.17580i	−0.120322	−	0.0694680i
$982$	−9.54541	+	5.51104i	−0.304606	+	0.175864i
$983$	−6.88388	+	3.97441i	−0.219562	+	0.126764i	−0.605747	−	0.795657i	$-0.707126\pi$
$983$	−6.88388	+	3.97441i	−0.219562	+	0.126764i	0.386186	+	0.922421i	$0.373792\pi$
$984$	5.23382			0.166848
$985$	−32.5517			−1.03718
$986$	7.52152	−	4.34255i	0.239534	−	0.138295i
$987$	−6.32282	−	1.11424i	−0.201258	−	0.0354668i
$988$	1.66571	−	2.02846i	0.0529934	−	0.0645338i
$989$	−8.99801	+	15.5850i	−0.286120	+	0.495575i
$990$	−4.22350	−	2.43844i	−0.134232	−	0.0774986i
$991$	−14.2131	+	24.6177i	−0.451493	+	0.782008i	−0.998479	−	0.0551333i	$-0.982442\pi$
$991$	−14.2131	+	24.6177i	−0.451493	+	0.782008i	0.546986	+	0.837142i	$0.315775\pi$
$992$	29.4272	+	50.9694i	0.934314	+	1.61828i
$993$			17.9518i			0.569683i
$994$	22.8894	−	8.33363i	0.726009	−	0.264327i
$995$	1.45752	+	0.841497i	0.0462064	+	0.0266773i
$996$	−10.1523	−	5.86141i	−0.321686	−	0.185726i
$997$	−44.8636			−1.42084			−0.710422	−	0.703776i	$-0.751496\pi$
$997$	−44.8636			−1.42084			−0.710422	+	0.703776i	$0.751496\pi$
$998$	6.47855	−	11.2212i	0.205075	−	0.355200i
$999$		−	5.80975i		−	0.183812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.t.d.205.4	yes	20
3.2	odd	2		819.2.bm.g.478.7		20
7.4	even	3		273.2.bl.d.88.7	yes	20
13.4	even	6		273.2.bl.d.121.7	yes	20
21.11	odd	6		819.2.do.g.361.4		20
39.17	odd	6		819.2.do.g.667.4		20
91.4	even	6	inner	273.2.t.d.4.7	✓	20
273.95	odd	6		819.2.bm.g.550.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.d.4.7	✓	20	91.4	even	6	inner
273.2.t.d.205.4	yes	20	1.1	even	1	trivial
273.2.bl.d.88.7	yes	20	7.4	even	3
273.2.bl.d.121.7	yes	20	13.4	even	6
819.2.bm.g.478.7		20	3.2	odd	2
819.2.bm.g.550.4		20	273.95	odd	6
819.2.do.g.361.4		20	21.11	odd	6
819.2.do.g.667.4		20	39.17	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.871638i q^{2} +(0.500000 - 0.866025i) q^{3} +1.24025 q^{4} +(1.34003 + 0.773665i) q^{5} +(-0.754861 - 0.435819i) q^{6} +(-2.02693 - 1.70046i) q^{7} -2.82432i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-0.871638i q^{2} +(0.500000 - 0.866025i) q^{3} +1.24025 q^{4} +(1.34003 + 0.773665i) q^{5} +(-0.754861 - 0.435819i) q^{6} +(-2.02693 - 1.70046i) q^{7} -2.82432i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.674356 - 1.16802i) q^{10} +(3.13150 + 1.80798i) q^{11} +(0.620123 - 1.07408i) q^{12} +(-3.37483 + 1.26906i) q^{13} +(-1.48218 + 1.76675i) q^{14} +(1.34003 - 0.773665i) q^{15} +0.0187042 q^{16} +4.63205 q^{17} +(-0.754861 + 0.435819i) q^{18} +(-0.508319 + 0.293478i) q^{19} +(1.66196 + 0.959535i) q^{20} +(-2.48610 + 0.905145i) q^{21} +(1.57590 - 2.72954i) q^{22} -2.28523 q^{23} +(-2.44594 - 1.41216i) q^{24} +(-1.30289 - 2.25666i) q^{25} +(1.10616 + 2.94163i) q^{26} -1.00000 q^{27} +(-2.51389 - 2.10899i) q^{28} +(1.07556 + 1.86293i) q^{29} +(-0.674356 - 1.16802i) q^{30} +(-8.99732 + 5.19461i) q^{31} -5.66495i q^{32} +(3.13150 - 1.80798i) q^{33} -4.03747i q^{34} +(-1.40056 - 3.84682i) q^{35} +(-0.620123 - 1.07408i) q^{36} +5.80975i q^{37} +(0.255807 + 0.443071i) q^{38} +(-0.588380 + 3.55722i) q^{39} +(2.18508 - 3.78467i) q^{40} +(-1.60485 + 0.926561i) q^{41} +(0.788959 + 2.16698i) q^{42} +(3.93747 - 6.81990i) q^{43} +(3.88384 + 2.24233i) q^{44} -1.54733i q^{45} +1.99189i q^{46} +(2.10152 + 1.21331i) q^{47} +(0.00935211 - 0.0161983i) q^{48} +(1.21689 + 6.89342i) q^{49} +(-1.96699 + 1.13565i) q^{50} +(2.31602 - 4.01147i) q^{51} +(-4.18562 + 1.57394i) q^{52} +(6.49352 + 11.2471i) q^{53} +0.871638i q^{54} +(2.79753 + 4.84547i) q^{55} +(-4.80264 + 5.72471i) q^{56} +0.586956i q^{57} +(1.62380 - 0.937502i) q^{58} +5.41501i q^{59} +(1.66196 - 0.959535i) q^{60} +(4.85421 + 8.40774i) q^{61} +(4.52782 + 7.84241i) q^{62} +(-0.459174 + 2.60560i) q^{63} -4.90038 q^{64} +(-5.50419 - 0.910418i) q^{65} +(-1.57590 - 2.72954i) q^{66} +(-1.66329 - 0.960298i) q^{67} +5.74488 q^{68} +(-1.14261 + 1.97906i) q^{69} +(-3.35304 + 1.22078i) q^{70} +(-9.14766 - 5.28141i) q^{71} +(-2.44594 + 1.41216i) q^{72} +(-1.96780 + 1.13611i) q^{73} +5.06400 q^{74} -2.60577 q^{75} +(-0.630441 + 0.363985i) q^{76} +(-3.27296 - 8.98963i) q^{77} +(3.10061 + 0.512855i) q^{78} +(5.78378 - 10.0178i) q^{79} +(0.0250642 + 0.0144708i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.807626 + 1.39885i) q^{82} -9.45200i q^{83} +(-3.08338 + 1.12260i) q^{84} +(6.20707 + 3.58365i) q^{85} +(-5.94449 - 3.43205i) q^{86} +2.15113 q^{87} +(5.10631 - 8.84438i) q^{88} +12.6671i q^{89} -1.34871 q^{90} +(8.99853 + 3.16647i) q^{91} -2.83424 q^{92} +10.3892i q^{93} +(1.05757 - 1.83177i) q^{94} -0.908215 q^{95} +(-4.90599 - 2.83247i) q^{96} +(-14.3826 - 8.30380i) q^{97} +(6.00857 - 1.06069i) q^{98} -3.61595i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9	\( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9} + 2 q^{10} - 12 q^{11} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} + 42 q^{16} + 16 q^{17} + 3 q^{18} - 9 q^{19} - 5 q^{21} - 9 q^{22} - 36 q^{23} + 3 q^{24} + 12 q^{25} - 16 q^{26} - 20 q^{27} - 2 q^{28} - 3 q^{29} - 2 q^{30} - 18 q^{31} - 12 q^{33} + 18 q^{35} + 13 q^{36} + 9 q^{38} + 7 q^{39} + 5 q^{40} + 21 q^{41} + 16 q^{42} + 16 q^{43} - 6 q^{44} + 21 q^{47} + 21 q^{48} - 24 q^{49} - 54 q^{50} + 8 q^{51} - 41 q^{52} - 26 q^{53} + 17 q^{55} - 6 q^{56} + 42 q^{58} + 4 q^{62} - 7 q^{63} - 46 q^{64} - 50 q^{65} + 9 q^{66} - 3 q^{67} + 6 q^{68} - 18 q^{69} + 15 q^{71} + 3 q^{72} - 9 q^{73} + 12 q^{74} + 24 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} - 24 q^{80} - 10 q^{81} + 15 q^{82} + 41 q^{84} - 78 q^{85} + 3 q^{86} - 6 q^{87} - 22 q^{88} - 4 q^{90} + 4 q^{91} + 142 q^{92} + 36 q^{94} - 84 q^{95} - 24 q^{96} - 15 q^{97} + 81 q^{98}+O(q^{100}) \) 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9 + 2 * q^10 - 12 * q^11 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 + 42 * q^16 + 16 * q^17 + 3 * q^18 - 9 * q^19 - 5 * q^21 - 9 * q^22 - 36 * q^23 + 3 * q^24 + 12 * q^25 - 16 * q^26 - 20 * q^27 - 2 * q^28 - 3 * q^29 - 2 * q^30 - 18 * q^31 - 12 * q^33 + 18 * q^35 + 13 * q^36 + 9 * q^38 + 7 * q^39 + 5 * q^40 + 21 * q^41 + 16 * q^42 + 16 * q^43 - 6 * q^44 + 21 * q^47 + 21 * q^48 - 24 * q^49 - 54 * q^50 + 8 * q^51 - 41 * q^52 - 26 * q^53 + 17 * q^55 - 6 * q^56 + 42 * q^58 + 4 * q^62 - 7 * q^63 - 46 * q^64 - 50 * q^65 + 9 * q^66 - 3 * q^67 + 6 * q^68 - 18 * q^69 + 15 * q^71 + 3 * q^72 - 9 * q^73 + 12 * q^74 + 24 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 - 24 * q^80 - 10 * q^81 + 15 * q^82 + 41 * q^84 - 78 * q^85 + 3 * q^86 - 6 * q^87 - 22 * q^88 - 4 * q^90 + 4 * q^91 + 142 * q^92 + 36 * q^94 - 84 * q^95 - 24 * q^96 - 15 * q^97 + 81 * q^98

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